Research ArticleA Novel Dynamic Multicriteria Decision-Making Approach forLow-Carbon Supplier Selection of Low-Carbon BuildingsBased on Interval-Valued Triangular Fuzzy Numbers
Xia Cao Zeyu Xing Yuqi Sun and Shi Yin
School of Economics and Management Harbin Engineering University Harbin Heilongjiang 150001 China
Correspondence should be addressed to Zeyu Xing hrq962163com
Received 27 April 2018 Accepted 5 September 2018 Published 24 October 2018
Guest Editor Tayfun Dede
Copyright copy 2018 Xia Cao et alis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Due to the lack of natural resources and environmental problems which have been appearing increasingly low-carbon buildingsare more andmore involved in the construction industrye selection of low-carbon supplier is a significant part in the process oflow-carbon building construction projects In this paper we propose a novel dynamic multicriteria decision-making approach forlow-carbon supplier selection in the process of low-carbon building construction projects to deal with these problems First thepaper establishes 5 main criteria and 17 subcriteria for low-carbon supplier selection in the process of low-carbon buildingconstruction projects en a method considering interaction between criteria and the influence of constructors subjectivepreference and objective criteria information is proposed It uses the basic concept and properties of the interval-valued triangularfuzzy number intuitionistic fuzzy weighted Bonferroni means (IVTFNIFWBM) operators and the objective information entropyand TOPSIS-based Euclidean distance to calculate the comprehensive evaluation results of potential low-carbon suppliers eproposed method is much easier for constructors to select low-carbon supplier and make the localization of low-carbon suppliermore practical and accurate in the process of building construction projects Finally a case study about a low-carbon buildingproject is given to verify practicality and effectiveness of the proposed approach
1 Introduction
Low-carbon building has been a popular research topic fromacademic and industrial sectors in recent years Buildingsplay a central part in causing greenhouse gas (GHG)emissions and account for nearly 70 of GHG emissions inHong Kong and up to 40 of total energy consumption [1]ese facts show that low-carbon building plays an im-portant role in reducing the amount of GHG emissionsMany countries have launched a series of measures to reduceGHG emissions in the construction industry [2] To copewith pressure it is a vital factor to select their suitable low-carbon suppliers Many factors should be taken into accountin the process of low-carbon supplier selection as a complexmulticriteria decision-making (MCDM) problem [3]erefore it is critically important and necessary to studylow-carbon supplier selection in the process of low-carbonbuilding construction projects
Many scholars have stressed the importance of selectingsuitable criteria in the process of low-carbon supplier se-lection Lee et al [4] proposed 5 main criteria for supplierselection such as quality technology capability pollutioncontrol green products and green competencies Hsu et al[5] established 13 criteria of supplier selection with threemain criteria such as planning implementation andmanagement Kannan et al [6] and Tsui and Wen [7]thought low-carbon supplier selection should consider low-carbon criteria in environmental aspects such as wastereduction green technologies and the usage of ecodesignGurel et al [8] established 8 main criteria that include costdelivery quality service strategic alliance and pollutioncontrol Chen et al [9] proposed 20 criteria for supplierselection and evaluation criteria with two dimensions(economic criteria and environmental criteria) Yu et al [10]took the economic criteria and environmental criteria intoconsideration during low-carbon supplier selection
HindawiAdvances in Civil EngineeringVolume 2018 Article ID 7456830 16 pageshttpsdoiorg10115520187456830
Govindan and Sivakumar [11] took economics operationalfactors and environmental criteria into consideration Panget al [12] proposed 4 main criteria including production andservice However most of them focus on low-carbon supplychain management and the research on the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects is fairly rare Moreover comparingwith the traditional low-carbon supplier selection criteriaconstructors must pay special attention to the environ-mental capabilities low-carbon building technologies andsocial factors for low-carbon supplier selection criteria in theprocess of low-carbon building construction projects [13]is research takes these aspects into consideration whichhave been ignored in many studies such as an evaluationcriterion
In recent years extensive MADM methods have beenproposed for supplier selection Govindan et al [14] con-cluded that the most frequently used method is AHP(2778) followed by ANP (166) DEA (111) LP(876) TOPSIS (556) and multiobjective optimization(277) In addition many methods have been developed toselect suitable low-carbon supplier based on specificmethods that include fuzzy set theory [9 12 15 16 19]genetic algorithm [17ndash19] structural equation modeling andfuzzy logic [20] and artificial neural network [21 22] Huet al [23] proposed a multicriteria group decision-makingmethod with 2-tuple linguistic assessments for low-carbonsupplier selection under a fuzzy uncertain informationenvironment Qin et al [24] developed a new TODIMtechnique to select low-carbon supplier within the context ofinterval type-2 fuzzy sets Bakeshlou et al [25] presenteda multiobjective hybrid fuzzy linear programming model forlow-carbon supplier selection problem
However most of these methods which do not considerinteraction between criteria can lead to irrational decision-making of low-carbon supplier selection in the process oflow-carbon building construction projects In fact there isalways an interactive relationship between criteria of low-carbon supplier selection such as complementarity betweencriteria the redundancy of criteria and preference relationof criteria
e Bonferroni mean (BM) is a mean type aggregationtechnique which considers interaction between attributesthat makes it very useful in decision-making [26 27] enmany scholars proposed BM operator [26 27] IFBM op-erator [27 28] IFGBM operator [26 29 30] and WIFBMoperator [31 32] Unfortunately there still is a lack of furthertheory and method research on the TFNIFN based on BMoperator erefore this paper focuses on a dynamic mul-tiattribute decision-making method with interval-valuedtriangular fuzzy number intuitionistic fuzzy that considersinteraction between attributes
In real life past and current information should also beconsidered when conducting dynamic decision-making andhow to solve the problem of time sequences weight has be-come the key to solving the dynamic decision-makingproblem Scholars such as Wei [33] Park et al [34] andYin et al [35] have designed dynamic intuitionistic fuzzydecision models of time dimension At present some of the
commonly used time sequence weights are as follows thearithmetic progression and geometric progression method[36] the binomial distribution method [37] the normaldistributionmethod [38] the exponential distributionmethod[39] and the time sequence ideal solution method [40 41]ese methods provide a reference for solving the time se-quence weights in dynamic multiattribute decision-makingproblems but their weights fully based on objective assign-ment methods or decision makerrsquos subjective preference anddid not consider to combine objective assignment methodswith decision makerrsquos subjective preference In our paper weconstruct a comprehensive time weight while considering theobjective assignment information as well as subjective pref-erence In addition dynamic stochastic multiattributedecision-making problems possess a time dimension and anattribute dimension so determining attribute weights isa prerequisite for assembling the attribute information re-quired for the final decision-making result Relevant scholarshave developed a variety of methods for successfully de-termining attribute weight Wei [42] has designed a newmethod based on maximizing deviation and two-tuple Chenet al [43] have obtained attribute weights by solving the greyrelation function of attribute information per the grey cor-relation model and Wang et al [44] have proposed a methodby using hesitant fuzzy entropy Finally we provide a newmethod of calculating the attribute weight by objective in-formation entropy and TOPSIS-based Euclidean distance
e main contribution of this paper is developing a newdynamic MADM that considers interaction between criteriaunder time sequence for low-carbon supplier selection in theprocess of low-carbon building construction projects enew dynamic multiattribute decision-making method isproposed with the interval-valued triangular fuzzy numberintuitionistic fuzzy weighted Bonferroni means (IVTF-NIFWBM) operator that considers interaction between at-tributes under time-sequence is method puts forwardsome concepts of IVTFNIFWBM operator and proves thatTo calculate attribute weights we introduce the objectiveinformation entropy and TOPSIS-based Euclidean distanceand present a new weight calculation method of IVTF-NIFWBM Also the method constructs a comprehensivetime weight while considering the objective assignmentinformation as well as subjective preference and can reflectthe process of dynamic decision-making more compre-hensively and reasonable e proposed method has beensuccessfully implemented in case construction projects toselect the best low-carbon supplier Besides the developedmethod can be widely used as a structural model for low-carbon supplier selection in other industries
e structure of this paper is organized as follows eproposed methodological framework for low-carbon sup-plier evaluation and selection is presented in Section 2Section 3 establishes the criteria for low-carbon supplierselection in the process of low-carbon building constructionprojects Section 4 draws some related concepts of theproposed approach for low-carbon supplier selection Sec-tion 5 proposes a method that considers interaction betweencriteria under time sequence based on IVTFNIFWBM op-erator and comprehensive time sequence weighted
2 Advances in Civil Engineering
calculation model and a new method of attribute weightedbased on the objective information entropy and TOPSIS-based Euclidean distance for low-carbon supplier selectionSection 6 provides a real case study that concerns low-carbon supplier selection in the process of low-carbonbuilding construction projects In Section 7 we end thepaper by summarizing the conclusions
2 Methodological Framework for Low-CarbonSupplier Evaluation and Selection
e proposed framework for low-carbon supplier evaluationand selection of low-carbon buildings is illustrated in Figure 1and it mainly consists of three stages First the low-carbonsupplier selection criteria in the process of low-carbonbuilding construction projects are identified from the com-prehensive literature review on-site investigation and thepolicy analysis according to the triple bottom line principleVarious realistic features in supplier selection of low-carbonbuilding construction projects are considered Second thevalidity of low-carbon supplier selection criteria is assessed bysenior purchasing experts and project managers with rich civilindustry experience and then we further modify the low-carbon supplier selection criteria until the validity of criteria issatisfactory according to the feedbacks of experts and projectmanagers en the experts and project managers evaluatealternative low-carbon supplier e best alternative is se-lected via the interval-valued triangular fuzzy multicriteriadecision-making model which is mainly made up of fourprocedures including calculating attribute weight based onEntropy-TOPSIS calculating time weight based on timedegree and ideal solution calculating information contents byIVTFIFWBM operator and evaluating and selecting the bestlow-carbon supplier ese procedures of the fuzzy multi-criteria decision-making model will be introduced in Section5 in detail
3 Low-Carbon Supplier Evaluation Criteria
For most projects in the process of low-carbon buildingconstruction the successful implementation of a projectrequires selecting low-carbon supplier that contributes tothe project objective Low-carbon supply chain in theconstruction industry is a functional network structuremodel which consists of main parts of construction in-dustry with building units as the core and logistics capitalflow information flow and knowledge flow as the support inthe whole life cycle of building projects In this section wewill introduce the proposed criteria for low-carbon supplierselection based on above reviews and the identified criteriaWe establish 5 main criteria and 17 subcriteria forlow-carbon supplier selection in the process of low-carbonbuilding construction projects (Table 1)
Low-carbon materials information is the basic point forlow-carbon supplier selection in the process of low-carbonbuilding construction projects In buildingrsquos constructionprocess projects demand different product types such asdifferent types of concrete steel and templet and productstructure to guarantee the successful completion of
construction projects erefore low-carbon supplier selec-tion in the process of low-carbon building constructionprojects should focus on materials flexibility efficiency in-formation and other aspects of building materials It isparticularly important to provide constructors with highquality and inexpensive building materials or service such aspayment terms to meet the needs of constructor In additionthe low-carbon degree of building materials reflects its abilityof saving resources and reducing energy consumption and thehigher the low-carbon degree is the more application po-tential the building materials will have in the future Mean-while it also needs to improve service quality and userexperience and strengthens after sales service supporterefore building materials information is mainly reflectedfrom four aspects materials cost low-carbon degree of ma-terials materials quality and materials flexibility
In the complex and changing market environment thecompetitiveness of low-carbon supply chain in the con-struction industry depends on rapid response to the needs ofdifferent product types and product structure in buildingrsquosconstruction process High level of low-carbon business op-eration can contribute to reducing carbon emissions which canbe reflected by the level of low-carbon information sharing thecost control of transportation and the supply chain man-agement of construction industry In addition constructorsneed to consider the financial capability to reduce the risk ofcooperation between constructors and its suppliersrsquo protectionfor the successful completion of construction projects Herewe use level of low-carbon information sharing low-carbonlogistics financial capability and emergency response capa-bility to measure the supplierrsquos low-carbon business operation
In the construction industry the main purpose ofestablishing low-carbon supply chain is to establish co-operative alliance of construction industry which canreduce building materialsrsquo cost and obtain more income inprojects Cooperation potential is the premise of estab-lishing strategic alliance and strong cooperation intentionand long-time cooperation are the foundation of estab-lishing strategic alliance If constructors want to maintainthe long-term stability of low-carbon supply chain co-operation they should choose those suppliers who haveadvanced management and desire of low-carbon cooperationfor development We can measure potential for sustainablecooperation from these four aspects compatibility of low-carbon culture desire of low-carbon cooperation enterprisereputation and low-carbon image
Low-carbon culture can promote the implementation ofenterprise strategic objectives of sustainable developmentvirtually If the low-carbon culture between partners cannotbe integrated it means that it will lead to different valuesbetween constructors and suppliers en it may lead todispute on both sides of the fierce confrontation and evenrelationship broken Ecodesign of building materials canreduce environmental pollution in the production processand reduce carbon emissions In addition low-carboncertifications reflect the environmental management capa-bility of low-carbon supplier
Low-carbon technology capability which is used toevaluate whether the low-carbon supplier meets the
Advances in Civil Engineering 3
requirements of low-carbon building is increasingly crucialto successfully implement low-carbon building and attainsustainability goals Low-carbon building technologies areincorporated into building design and construction to makethe end product sustainable Low-carbon RampD innovationinclude new launch of building materials and low-carbonbuilding technologies and there are many dierent
low-carbon building technologies applicable in the wholeprocess of delivering building projects
4 Preliminaries
Here we introduce some basic concepts and terminologiesof intuitionistic fuzzy set (IFS) which will be used in theproposed method Its denition is introduced as follows
Table 1 Criteria for low-carbon supplier selection in the process of low-carbon building construction projects
Criteria Main criteria Subcriteria
Low-carbon supplier selection inthe process of low-carbon buildingconstruction projects
C1 low-carbon materials information
C11 materials costC12 low-carbon degree of materials
C13 materials qualityC14 materials exibility
C2 low-carbon business operation
C21 level of low-carbon information sharingC22 low-carbon logisticsC23 nancial capability
C24 emergency response capability
C3 potential for sustainable cooperationC31 desire of low-carbon cooperation
C32 enterprise reputationC33 low-carbon image
C4 low-carbon potentialC41 low-carbon certicationsC42 ecodesign of materials
C43 compatibility of low-carbon culture
C5 low-carbon technology capabilityC51 low-carbon production
Evaluating and selecting the bestlow carbon supplier
Calculating information contentsby IVTFIFWBM operator
Calculating attributeweight based on entropy-
TOPSIS
Calculating time weightbased on time degree and
ideal solution
Interval-valued triangular fuzzy multicriteriadecision-making model
Low carbon supplierselection criteria
Literaturereview
On-siteinvestigation
Policyanalysis
Project managers and experts evaluatealternative suppliers through interval-valued
triangular fuzzy numbers
Figure 1 Methodological framework for low-carbon supplier evaluation and selection
4 Advances in Civil Engineering
Definition 1 Let A as an intuitionistic fuzzy set (IFS)and A langx uA(x) vA(x)rang1113864 1113865x isin X with the conditionthat [45]
uA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
vA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
0le uA(x) + vA(x)le 1 x isin X
(1)
We can find that an IFS is constructed by twoinformation functions which not only describe themembership degree uA(x) but also describe the non-membership degree vA(x) Moreover the hesitancy in-formation of x isin X can be denoted by πA(x) 1minusuA(x)minus vA(x) which is called the hesitant index andtherefore IFS can describe the uncertainty and fuzzinessmore objectively than the usual fuzzy set
Definition 2 Zadeh first proposed the concept of triangularfuzzy number [43] Let X as a nonempty finite set A tri-angular fuzzy number intuitionistic fuzzy set (TFNIFS) A inX is defined as X langx 1113954uA(x) 1113954vA(x)rang|x isin X1113864 1113865 where 1113954uA
[1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] and 1113954vA [1113954vl
A(x) 1113954vmA (x) 1113954vu
A(x)] de-note respectively membership and nonmembership of theelement x in X to A and
0le 1113954uuA(x) + 1113954v
uA(x)le 1 1113954u
lA(x)ge 0 1113954v
lA(x)ge 0 (2)
en we call ([1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] [1113954vl
A(x) 1113954vmA (x)
1113954vuA(x)]) as an IVTFNIFN and it is also called as ([a
b c] [d e f]) [46]
Definition 3 Let 1113957α1 ([a1 b1 c1] [d1 e1 f1]) and 1113957α2
([a2 b2 c2] [d2 e2 f2]) are two random IVTFNIFN then
1113957α1 oplus 1113957α2 ( a1 + a2 minus a1a2 b1 + b2 minus b1b2 c1 + c2 minus c1c21113858 1113859
d1d2 e1e2 f1f21113858 11138591113857
(3)
1113957α1 otimes 1113957α2 1113874 a1a2 b1b2 c1c21113858 1113859 1113858d1 + d2 minus d1d2 e1 + e2 minus e1e2
Definition 4 For any IVTFNIFN 1113957α ([a b c] [d e f])the score of 1113957α can be evaluated by the score function S asfollows [47]
S(1113957α) a + 2b + c
4minus
d + 2e + f
4 (7)
where S(1113957α) isin [minus1 1]And an accuracy function is shown below
H(1113957α) a + 2b + c
42minus
a + 2b + c
4minus
d + 2e + f
41113888 1113889 (8)
Definition 5 Suppose 1113957α1 and 1113957α2 are two IVTFNIFN [48] where
(1) If S(1113957α1)≺ S(1113957α2) then 1113957α1 ≺ 1113957α2(2) If S(1113957α1) S(1113957α2) and when H(1113957α1)≺H(1113957α2) then
1113957α1 ≺ 1113957α2 when H(1113957α1) H(1113957α2) then 1113957α1 1113957α2
5 The Proposed Approach for Low-CarbonSuppliers Selection
51 Low-Carbon Suppliers Problem Description To thelow-carbon supplier selection problem in the process oflow-carbon building construction projects for which Si
S1 S2 Sm1113864 1113865(mge 2) is a discrete and feasible alterna-tive solution set of low-carbon suppliers Cj C11113864
C2 Cn(nge 2) is the finite set of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects w (w1 w2 wn)T is a weightvector which satisfies 0lewj le 1 1113936
nj1wj 1 and η(tk)
(η(t1) η(t2) η(tψ))T is the time weight vector where0le η(tk)le 1 and 1113936
ψk1η(tk) 1 e value of criteria Cj to
which solution Si is subject at moment tk is denoted asXij(tk) which is subject to an interval-valued triangularintuitionistic fuzzy denoted as Xij(tk) sim ηij(tk)
fij(tk)])mtimesn based on ψ moment of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Low-carbon supplier selectionproblems consist of multiple dimensions such as suppliercriteria and time Integration operator and determiningtime sequence weight are important technologies to re-duce dimensionality and solve low-carbon supplier se-lection problem under interval-valued intuitionistic fuzzyenvironment
52 Interval-Valued Triangular Fuzzy Number IntuitionisticFuzzy Bonferroni Means Operator
Definition 6 Let p qge 0 and ai(i 1 2 n) be a collec-tion of nonnegative numbers [48] If
Bpq
a1 a2 an( 1113857 1
n(nminus 1)1113944
n
ij1inej
api a
qj
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
1p+q
(9)
then Bpq is called the Bonferroni mean (BM)
Definition 7 Let 1113957αi ([ai bi ci] [di ei fi]) as a collection ofIVTFNIFNs For any p q≻0 if
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
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Submit your manuscripts atwwwhindawicom
Govindan and Sivakumar [11] took economics operationalfactors and environmental criteria into consideration Panget al [12] proposed 4 main criteria including production andservice However most of them focus on low-carbon supplychain management and the research on the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects is fairly rare Moreover comparingwith the traditional low-carbon supplier selection criteriaconstructors must pay special attention to the environ-mental capabilities low-carbon building technologies andsocial factors for low-carbon supplier selection criteria in theprocess of low-carbon building construction projects [13]is research takes these aspects into consideration whichhave been ignored in many studies such as an evaluationcriterion
In recent years extensive MADM methods have beenproposed for supplier selection Govindan et al [14] con-cluded that the most frequently used method is AHP(2778) followed by ANP (166) DEA (111) LP(876) TOPSIS (556) and multiobjective optimization(277) In addition many methods have been developed toselect suitable low-carbon supplier based on specificmethods that include fuzzy set theory [9 12 15 16 19]genetic algorithm [17ndash19] structural equation modeling andfuzzy logic [20] and artificial neural network [21 22] Huet al [23] proposed a multicriteria group decision-makingmethod with 2-tuple linguistic assessments for low-carbonsupplier selection under a fuzzy uncertain informationenvironment Qin et al [24] developed a new TODIMtechnique to select low-carbon supplier within the context ofinterval type-2 fuzzy sets Bakeshlou et al [25] presenteda multiobjective hybrid fuzzy linear programming model forlow-carbon supplier selection problem
However most of these methods which do not considerinteraction between criteria can lead to irrational decision-making of low-carbon supplier selection in the process oflow-carbon building construction projects In fact there isalways an interactive relationship between criteria of low-carbon supplier selection such as complementarity betweencriteria the redundancy of criteria and preference relationof criteria
e Bonferroni mean (BM) is a mean type aggregationtechnique which considers interaction between attributesthat makes it very useful in decision-making [26 27] enmany scholars proposed BM operator [26 27] IFBM op-erator [27 28] IFGBM operator [26 29 30] and WIFBMoperator [31 32] Unfortunately there still is a lack of furthertheory and method research on the TFNIFN based on BMoperator erefore this paper focuses on a dynamic mul-tiattribute decision-making method with interval-valuedtriangular fuzzy number intuitionistic fuzzy that considersinteraction between attributes
In real life past and current information should also beconsidered when conducting dynamic decision-making andhow to solve the problem of time sequences weight has be-come the key to solving the dynamic decision-makingproblem Scholars such as Wei [33] Park et al [34] andYin et al [35] have designed dynamic intuitionistic fuzzydecision models of time dimension At present some of the
commonly used time sequence weights are as follows thearithmetic progression and geometric progression method[36] the binomial distribution method [37] the normaldistributionmethod [38] the exponential distributionmethod[39] and the time sequence ideal solution method [40 41]ese methods provide a reference for solving the time se-quence weights in dynamic multiattribute decision-makingproblems but their weights fully based on objective assign-ment methods or decision makerrsquos subjective preference anddid not consider to combine objective assignment methodswith decision makerrsquos subjective preference In our paper weconstruct a comprehensive time weight while considering theobjective assignment information as well as subjective pref-erence In addition dynamic stochastic multiattributedecision-making problems possess a time dimension and anattribute dimension so determining attribute weights isa prerequisite for assembling the attribute information re-quired for the final decision-making result Relevant scholarshave developed a variety of methods for successfully de-termining attribute weight Wei [42] has designed a newmethod based on maximizing deviation and two-tuple Chenet al [43] have obtained attribute weights by solving the greyrelation function of attribute information per the grey cor-relation model and Wang et al [44] have proposed a methodby using hesitant fuzzy entropy Finally we provide a newmethod of calculating the attribute weight by objective in-formation entropy and TOPSIS-based Euclidean distance
e main contribution of this paper is developing a newdynamic MADM that considers interaction between criteriaunder time sequence for low-carbon supplier selection in theprocess of low-carbon building construction projects enew dynamic multiattribute decision-making method isproposed with the interval-valued triangular fuzzy numberintuitionistic fuzzy weighted Bonferroni means (IVTF-NIFWBM) operator that considers interaction between at-tributes under time-sequence is method puts forwardsome concepts of IVTFNIFWBM operator and proves thatTo calculate attribute weights we introduce the objectiveinformation entropy and TOPSIS-based Euclidean distanceand present a new weight calculation method of IVTF-NIFWBM Also the method constructs a comprehensivetime weight while considering the objective assignmentinformation as well as subjective preference and can reflectthe process of dynamic decision-making more compre-hensively and reasonable e proposed method has beensuccessfully implemented in case construction projects toselect the best low-carbon supplier Besides the developedmethod can be widely used as a structural model for low-carbon supplier selection in other industries
e structure of this paper is organized as follows eproposed methodological framework for low-carbon sup-plier evaluation and selection is presented in Section 2Section 3 establishes the criteria for low-carbon supplierselection in the process of low-carbon building constructionprojects Section 4 draws some related concepts of theproposed approach for low-carbon supplier selection Sec-tion 5 proposes a method that considers interaction betweencriteria under time sequence based on IVTFNIFWBM op-erator and comprehensive time sequence weighted
2 Advances in Civil Engineering
calculation model and a new method of attribute weightedbased on the objective information entropy and TOPSIS-based Euclidean distance for low-carbon supplier selectionSection 6 provides a real case study that concerns low-carbon supplier selection in the process of low-carbonbuilding construction projects In Section 7 we end thepaper by summarizing the conclusions
2 Methodological Framework for Low-CarbonSupplier Evaluation and Selection
e proposed framework for low-carbon supplier evaluationand selection of low-carbon buildings is illustrated in Figure 1and it mainly consists of three stages First the low-carbonsupplier selection criteria in the process of low-carbonbuilding construction projects are identified from the com-prehensive literature review on-site investigation and thepolicy analysis according to the triple bottom line principleVarious realistic features in supplier selection of low-carbonbuilding construction projects are considered Second thevalidity of low-carbon supplier selection criteria is assessed bysenior purchasing experts and project managers with rich civilindustry experience and then we further modify the low-carbon supplier selection criteria until the validity of criteria issatisfactory according to the feedbacks of experts and projectmanagers en the experts and project managers evaluatealternative low-carbon supplier e best alternative is se-lected via the interval-valued triangular fuzzy multicriteriadecision-making model which is mainly made up of fourprocedures including calculating attribute weight based onEntropy-TOPSIS calculating time weight based on timedegree and ideal solution calculating information contents byIVTFIFWBM operator and evaluating and selecting the bestlow-carbon supplier ese procedures of the fuzzy multi-criteria decision-making model will be introduced in Section5 in detail
3 Low-Carbon Supplier Evaluation Criteria
For most projects in the process of low-carbon buildingconstruction the successful implementation of a projectrequires selecting low-carbon supplier that contributes tothe project objective Low-carbon supply chain in theconstruction industry is a functional network structuremodel which consists of main parts of construction in-dustry with building units as the core and logistics capitalflow information flow and knowledge flow as the support inthe whole life cycle of building projects In this section wewill introduce the proposed criteria for low-carbon supplierselection based on above reviews and the identified criteriaWe establish 5 main criteria and 17 subcriteria forlow-carbon supplier selection in the process of low-carbonbuilding construction projects (Table 1)
Low-carbon materials information is the basic point forlow-carbon supplier selection in the process of low-carbonbuilding construction projects In buildingrsquos constructionprocess projects demand different product types such asdifferent types of concrete steel and templet and productstructure to guarantee the successful completion of
construction projects erefore low-carbon supplier selec-tion in the process of low-carbon building constructionprojects should focus on materials flexibility efficiency in-formation and other aspects of building materials It isparticularly important to provide constructors with highquality and inexpensive building materials or service such aspayment terms to meet the needs of constructor In additionthe low-carbon degree of building materials reflects its abilityof saving resources and reducing energy consumption and thehigher the low-carbon degree is the more application po-tential the building materials will have in the future Mean-while it also needs to improve service quality and userexperience and strengthens after sales service supporterefore building materials information is mainly reflectedfrom four aspects materials cost low-carbon degree of ma-terials materials quality and materials flexibility
In the complex and changing market environment thecompetitiveness of low-carbon supply chain in the con-struction industry depends on rapid response to the needs ofdifferent product types and product structure in buildingrsquosconstruction process High level of low-carbon business op-eration can contribute to reducing carbon emissions which canbe reflected by the level of low-carbon information sharing thecost control of transportation and the supply chain man-agement of construction industry In addition constructorsneed to consider the financial capability to reduce the risk ofcooperation between constructors and its suppliersrsquo protectionfor the successful completion of construction projects Herewe use level of low-carbon information sharing low-carbonlogistics financial capability and emergency response capa-bility to measure the supplierrsquos low-carbon business operation
In the construction industry the main purpose ofestablishing low-carbon supply chain is to establish co-operative alliance of construction industry which canreduce building materialsrsquo cost and obtain more income inprojects Cooperation potential is the premise of estab-lishing strategic alliance and strong cooperation intentionand long-time cooperation are the foundation of estab-lishing strategic alliance If constructors want to maintainthe long-term stability of low-carbon supply chain co-operation they should choose those suppliers who haveadvanced management and desire of low-carbon cooperationfor development We can measure potential for sustainablecooperation from these four aspects compatibility of low-carbon culture desire of low-carbon cooperation enterprisereputation and low-carbon image
Low-carbon culture can promote the implementation ofenterprise strategic objectives of sustainable developmentvirtually If the low-carbon culture between partners cannotbe integrated it means that it will lead to different valuesbetween constructors and suppliers en it may lead todispute on both sides of the fierce confrontation and evenrelationship broken Ecodesign of building materials canreduce environmental pollution in the production processand reduce carbon emissions In addition low-carboncertifications reflect the environmental management capa-bility of low-carbon supplier
Low-carbon technology capability which is used toevaluate whether the low-carbon supplier meets the
Advances in Civil Engineering 3
requirements of low-carbon building is increasingly crucialto successfully implement low-carbon building and attainsustainability goals Low-carbon building technologies areincorporated into building design and construction to makethe end product sustainable Low-carbon RampD innovationinclude new launch of building materials and low-carbonbuilding technologies and there are many dierent
low-carbon building technologies applicable in the wholeprocess of delivering building projects
4 Preliminaries
Here we introduce some basic concepts and terminologiesof intuitionistic fuzzy set (IFS) which will be used in theproposed method Its denition is introduced as follows
Table 1 Criteria for low-carbon supplier selection in the process of low-carbon building construction projects
Criteria Main criteria Subcriteria
Low-carbon supplier selection inthe process of low-carbon buildingconstruction projects
C1 low-carbon materials information
C11 materials costC12 low-carbon degree of materials
C13 materials qualityC14 materials exibility
C2 low-carbon business operation
C21 level of low-carbon information sharingC22 low-carbon logisticsC23 nancial capability
C24 emergency response capability
C3 potential for sustainable cooperationC31 desire of low-carbon cooperation
C32 enterprise reputationC33 low-carbon image
C4 low-carbon potentialC41 low-carbon certicationsC42 ecodesign of materials
C43 compatibility of low-carbon culture
C5 low-carbon technology capabilityC51 low-carbon production
Evaluating and selecting the bestlow carbon supplier
Calculating information contentsby IVTFIFWBM operator
Calculating attributeweight based on entropy-
TOPSIS
Calculating time weightbased on time degree and
ideal solution
Interval-valued triangular fuzzy multicriteriadecision-making model
Low carbon supplierselection criteria
Literaturereview
On-siteinvestigation
Policyanalysis
Project managers and experts evaluatealternative suppliers through interval-valued
triangular fuzzy numbers
Figure 1 Methodological framework for low-carbon supplier evaluation and selection
4 Advances in Civil Engineering
Definition 1 Let A as an intuitionistic fuzzy set (IFS)and A langx uA(x) vA(x)rang1113864 1113865x isin X with the conditionthat [45]
uA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
vA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
0le uA(x) + vA(x)le 1 x isin X
(1)
We can find that an IFS is constructed by twoinformation functions which not only describe themembership degree uA(x) but also describe the non-membership degree vA(x) Moreover the hesitancy in-formation of x isin X can be denoted by πA(x) 1minusuA(x)minus vA(x) which is called the hesitant index andtherefore IFS can describe the uncertainty and fuzzinessmore objectively than the usual fuzzy set
Definition 2 Zadeh first proposed the concept of triangularfuzzy number [43] Let X as a nonempty finite set A tri-angular fuzzy number intuitionistic fuzzy set (TFNIFS) A inX is defined as X langx 1113954uA(x) 1113954vA(x)rang|x isin X1113864 1113865 where 1113954uA
[1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] and 1113954vA [1113954vl
A(x) 1113954vmA (x) 1113954vu
A(x)] de-note respectively membership and nonmembership of theelement x in X to A and
0le 1113954uuA(x) + 1113954v
uA(x)le 1 1113954u
lA(x)ge 0 1113954v
lA(x)ge 0 (2)
en we call ([1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] [1113954vl
A(x) 1113954vmA (x)
1113954vuA(x)]) as an IVTFNIFN and it is also called as ([a
b c] [d e f]) [46]
Definition 3 Let 1113957α1 ([a1 b1 c1] [d1 e1 f1]) and 1113957α2
([a2 b2 c2] [d2 e2 f2]) are two random IVTFNIFN then
1113957α1 oplus 1113957α2 ( a1 + a2 minus a1a2 b1 + b2 minus b1b2 c1 + c2 minus c1c21113858 1113859
d1d2 e1e2 f1f21113858 11138591113857
(3)
1113957α1 otimes 1113957α2 1113874 a1a2 b1b2 c1c21113858 1113859 1113858d1 + d2 minus d1d2 e1 + e2 minus e1e2
Definition 4 For any IVTFNIFN 1113957α ([a b c] [d e f])the score of 1113957α can be evaluated by the score function S asfollows [47]
S(1113957α) a + 2b + c
4minus
d + 2e + f
4 (7)
where S(1113957α) isin [minus1 1]And an accuracy function is shown below
H(1113957α) a + 2b + c
42minus
a + 2b + c
4minus
d + 2e + f
41113888 1113889 (8)
Definition 5 Suppose 1113957α1 and 1113957α2 are two IVTFNIFN [48] where
(1) If S(1113957α1)≺ S(1113957α2) then 1113957α1 ≺ 1113957α2(2) If S(1113957α1) S(1113957α2) and when H(1113957α1)≺H(1113957α2) then
1113957α1 ≺ 1113957α2 when H(1113957α1) H(1113957α2) then 1113957α1 1113957α2
5 The Proposed Approach for Low-CarbonSuppliers Selection
51 Low-Carbon Suppliers Problem Description To thelow-carbon supplier selection problem in the process oflow-carbon building construction projects for which Si
S1 S2 Sm1113864 1113865(mge 2) is a discrete and feasible alterna-tive solution set of low-carbon suppliers Cj C11113864
C2 Cn(nge 2) is the finite set of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects w (w1 w2 wn)T is a weightvector which satisfies 0lewj le 1 1113936
nj1wj 1 and η(tk)
(η(t1) η(t2) η(tψ))T is the time weight vector where0le η(tk)le 1 and 1113936
ψk1η(tk) 1 e value of criteria Cj to
which solution Si is subject at moment tk is denoted asXij(tk) which is subject to an interval-valued triangularintuitionistic fuzzy denoted as Xij(tk) sim ηij(tk)
fij(tk)])mtimesn based on ψ moment of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Low-carbon supplier selectionproblems consist of multiple dimensions such as suppliercriteria and time Integration operator and determiningtime sequence weight are important technologies to re-duce dimensionality and solve low-carbon supplier se-lection problem under interval-valued intuitionistic fuzzyenvironment
52 Interval-Valued Triangular Fuzzy Number IntuitionisticFuzzy Bonferroni Means Operator
Definition 6 Let p qge 0 and ai(i 1 2 n) be a collec-tion of nonnegative numbers [48] If
Bpq
a1 a2 an( 1113857 1
n(nminus 1)1113944
n
ij1inej
api a
qj
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
1p+q
(9)
then Bpq is called the Bonferroni mean (BM)
Definition 7 Let 1113957αi ([ai bi ci] [di ei fi]) as a collection ofIVTFNIFNs For any p q≻0 if
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
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calculation model and a new method of attribute weightedbased on the objective information entropy and TOPSIS-based Euclidean distance for low-carbon supplier selectionSection 6 provides a real case study that concerns low-carbon supplier selection in the process of low-carbonbuilding construction projects In Section 7 we end thepaper by summarizing the conclusions
2 Methodological Framework for Low-CarbonSupplier Evaluation and Selection
e proposed framework for low-carbon supplier evaluationand selection of low-carbon buildings is illustrated in Figure 1and it mainly consists of three stages First the low-carbonsupplier selection criteria in the process of low-carbonbuilding construction projects are identified from the com-prehensive literature review on-site investigation and thepolicy analysis according to the triple bottom line principleVarious realistic features in supplier selection of low-carbonbuilding construction projects are considered Second thevalidity of low-carbon supplier selection criteria is assessed bysenior purchasing experts and project managers with rich civilindustry experience and then we further modify the low-carbon supplier selection criteria until the validity of criteria issatisfactory according to the feedbacks of experts and projectmanagers en the experts and project managers evaluatealternative low-carbon supplier e best alternative is se-lected via the interval-valued triangular fuzzy multicriteriadecision-making model which is mainly made up of fourprocedures including calculating attribute weight based onEntropy-TOPSIS calculating time weight based on timedegree and ideal solution calculating information contents byIVTFIFWBM operator and evaluating and selecting the bestlow-carbon supplier ese procedures of the fuzzy multi-criteria decision-making model will be introduced in Section5 in detail
3 Low-Carbon Supplier Evaluation Criteria
For most projects in the process of low-carbon buildingconstruction the successful implementation of a projectrequires selecting low-carbon supplier that contributes tothe project objective Low-carbon supply chain in theconstruction industry is a functional network structuremodel which consists of main parts of construction in-dustry with building units as the core and logistics capitalflow information flow and knowledge flow as the support inthe whole life cycle of building projects In this section wewill introduce the proposed criteria for low-carbon supplierselection based on above reviews and the identified criteriaWe establish 5 main criteria and 17 subcriteria forlow-carbon supplier selection in the process of low-carbonbuilding construction projects (Table 1)
Low-carbon materials information is the basic point forlow-carbon supplier selection in the process of low-carbonbuilding construction projects In buildingrsquos constructionprocess projects demand different product types such asdifferent types of concrete steel and templet and productstructure to guarantee the successful completion of
construction projects erefore low-carbon supplier selec-tion in the process of low-carbon building constructionprojects should focus on materials flexibility efficiency in-formation and other aspects of building materials It isparticularly important to provide constructors with highquality and inexpensive building materials or service such aspayment terms to meet the needs of constructor In additionthe low-carbon degree of building materials reflects its abilityof saving resources and reducing energy consumption and thehigher the low-carbon degree is the more application po-tential the building materials will have in the future Mean-while it also needs to improve service quality and userexperience and strengthens after sales service supporterefore building materials information is mainly reflectedfrom four aspects materials cost low-carbon degree of ma-terials materials quality and materials flexibility
In the complex and changing market environment thecompetitiveness of low-carbon supply chain in the con-struction industry depends on rapid response to the needs ofdifferent product types and product structure in buildingrsquosconstruction process High level of low-carbon business op-eration can contribute to reducing carbon emissions which canbe reflected by the level of low-carbon information sharing thecost control of transportation and the supply chain man-agement of construction industry In addition constructorsneed to consider the financial capability to reduce the risk ofcooperation between constructors and its suppliersrsquo protectionfor the successful completion of construction projects Herewe use level of low-carbon information sharing low-carbonlogistics financial capability and emergency response capa-bility to measure the supplierrsquos low-carbon business operation
In the construction industry the main purpose ofestablishing low-carbon supply chain is to establish co-operative alliance of construction industry which canreduce building materialsrsquo cost and obtain more income inprojects Cooperation potential is the premise of estab-lishing strategic alliance and strong cooperation intentionand long-time cooperation are the foundation of estab-lishing strategic alliance If constructors want to maintainthe long-term stability of low-carbon supply chain co-operation they should choose those suppliers who haveadvanced management and desire of low-carbon cooperationfor development We can measure potential for sustainablecooperation from these four aspects compatibility of low-carbon culture desire of low-carbon cooperation enterprisereputation and low-carbon image
Low-carbon culture can promote the implementation ofenterprise strategic objectives of sustainable developmentvirtually If the low-carbon culture between partners cannotbe integrated it means that it will lead to different valuesbetween constructors and suppliers en it may lead todispute on both sides of the fierce confrontation and evenrelationship broken Ecodesign of building materials canreduce environmental pollution in the production processand reduce carbon emissions In addition low-carboncertifications reflect the environmental management capa-bility of low-carbon supplier
Low-carbon technology capability which is used toevaluate whether the low-carbon supplier meets the
Advances in Civil Engineering 3
requirements of low-carbon building is increasingly crucialto successfully implement low-carbon building and attainsustainability goals Low-carbon building technologies areincorporated into building design and construction to makethe end product sustainable Low-carbon RampD innovationinclude new launch of building materials and low-carbonbuilding technologies and there are many dierent
low-carbon building technologies applicable in the wholeprocess of delivering building projects
4 Preliminaries
Here we introduce some basic concepts and terminologiesof intuitionistic fuzzy set (IFS) which will be used in theproposed method Its denition is introduced as follows
Table 1 Criteria for low-carbon supplier selection in the process of low-carbon building construction projects
Criteria Main criteria Subcriteria
Low-carbon supplier selection inthe process of low-carbon buildingconstruction projects
C1 low-carbon materials information
C11 materials costC12 low-carbon degree of materials
C13 materials qualityC14 materials exibility
C2 low-carbon business operation
C21 level of low-carbon information sharingC22 low-carbon logisticsC23 nancial capability
C24 emergency response capability
C3 potential for sustainable cooperationC31 desire of low-carbon cooperation
C32 enterprise reputationC33 low-carbon image
C4 low-carbon potentialC41 low-carbon certicationsC42 ecodesign of materials
C43 compatibility of low-carbon culture
C5 low-carbon technology capabilityC51 low-carbon production
Evaluating and selecting the bestlow carbon supplier
Calculating information contentsby IVTFIFWBM operator
Calculating attributeweight based on entropy-
TOPSIS
Calculating time weightbased on time degree and
ideal solution
Interval-valued triangular fuzzy multicriteriadecision-making model
Low carbon supplierselection criteria
Literaturereview
On-siteinvestigation
Policyanalysis
Project managers and experts evaluatealternative suppliers through interval-valued
triangular fuzzy numbers
Figure 1 Methodological framework for low-carbon supplier evaluation and selection
4 Advances in Civil Engineering
Definition 1 Let A as an intuitionistic fuzzy set (IFS)and A langx uA(x) vA(x)rang1113864 1113865x isin X with the conditionthat [45]
uA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
vA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
0le uA(x) + vA(x)le 1 x isin X
(1)
We can find that an IFS is constructed by twoinformation functions which not only describe themembership degree uA(x) but also describe the non-membership degree vA(x) Moreover the hesitancy in-formation of x isin X can be denoted by πA(x) 1minusuA(x)minus vA(x) which is called the hesitant index andtherefore IFS can describe the uncertainty and fuzzinessmore objectively than the usual fuzzy set
Definition 2 Zadeh first proposed the concept of triangularfuzzy number [43] Let X as a nonempty finite set A tri-angular fuzzy number intuitionistic fuzzy set (TFNIFS) A inX is defined as X langx 1113954uA(x) 1113954vA(x)rang|x isin X1113864 1113865 where 1113954uA
[1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] and 1113954vA [1113954vl
A(x) 1113954vmA (x) 1113954vu
A(x)] de-note respectively membership and nonmembership of theelement x in X to A and
0le 1113954uuA(x) + 1113954v
uA(x)le 1 1113954u
lA(x)ge 0 1113954v
lA(x)ge 0 (2)
en we call ([1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] [1113954vl
A(x) 1113954vmA (x)
1113954vuA(x)]) as an IVTFNIFN and it is also called as ([a
b c] [d e f]) [46]
Definition 3 Let 1113957α1 ([a1 b1 c1] [d1 e1 f1]) and 1113957α2
([a2 b2 c2] [d2 e2 f2]) are two random IVTFNIFN then
1113957α1 oplus 1113957α2 ( a1 + a2 minus a1a2 b1 + b2 minus b1b2 c1 + c2 minus c1c21113858 1113859
d1d2 e1e2 f1f21113858 11138591113857
(3)
1113957α1 otimes 1113957α2 1113874 a1a2 b1b2 c1c21113858 1113859 1113858d1 + d2 minus d1d2 e1 + e2 minus e1e2
Definition 4 For any IVTFNIFN 1113957α ([a b c] [d e f])the score of 1113957α can be evaluated by the score function S asfollows [47]
S(1113957α) a + 2b + c
4minus
d + 2e + f
4 (7)
where S(1113957α) isin [minus1 1]And an accuracy function is shown below
H(1113957α) a + 2b + c
42minus
a + 2b + c
4minus
d + 2e + f
41113888 1113889 (8)
Definition 5 Suppose 1113957α1 and 1113957α2 are two IVTFNIFN [48] where
(1) If S(1113957α1)≺ S(1113957α2) then 1113957α1 ≺ 1113957α2(2) If S(1113957α1) S(1113957α2) and when H(1113957α1)≺H(1113957α2) then
1113957α1 ≺ 1113957α2 when H(1113957α1) H(1113957α2) then 1113957α1 1113957α2
5 The Proposed Approach for Low-CarbonSuppliers Selection
51 Low-Carbon Suppliers Problem Description To thelow-carbon supplier selection problem in the process oflow-carbon building construction projects for which Si
S1 S2 Sm1113864 1113865(mge 2) is a discrete and feasible alterna-tive solution set of low-carbon suppliers Cj C11113864
C2 Cn(nge 2) is the finite set of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects w (w1 w2 wn)T is a weightvector which satisfies 0lewj le 1 1113936
nj1wj 1 and η(tk)
(η(t1) η(t2) η(tψ))T is the time weight vector where0le η(tk)le 1 and 1113936
ψk1η(tk) 1 e value of criteria Cj to
which solution Si is subject at moment tk is denoted asXij(tk) which is subject to an interval-valued triangularintuitionistic fuzzy denoted as Xij(tk) sim ηij(tk)
fij(tk)])mtimesn based on ψ moment of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Low-carbon supplier selectionproblems consist of multiple dimensions such as suppliercriteria and time Integration operator and determiningtime sequence weight are important technologies to re-duce dimensionality and solve low-carbon supplier se-lection problem under interval-valued intuitionistic fuzzyenvironment
52 Interval-Valued Triangular Fuzzy Number IntuitionisticFuzzy Bonferroni Means Operator
Definition 6 Let p qge 0 and ai(i 1 2 n) be a collec-tion of nonnegative numbers [48] If
Bpq
a1 a2 an( 1113857 1
n(nminus 1)1113944
n
ij1inej
api a
qj
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
1p+q
(9)
then Bpq is called the Bonferroni mean (BM)
Definition 7 Let 1113957αi ([ai bi ci] [di ei fi]) as a collection ofIVTFNIFNs For any p q≻0 if
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
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Navigation and Observation
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Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
requirements of low-carbon building is increasingly crucialto successfully implement low-carbon building and attainsustainability goals Low-carbon building technologies areincorporated into building design and construction to makethe end product sustainable Low-carbon RampD innovationinclude new launch of building materials and low-carbonbuilding technologies and there are many dierent
low-carbon building technologies applicable in the wholeprocess of delivering building projects
4 Preliminaries
Here we introduce some basic concepts and terminologiesof intuitionistic fuzzy set (IFS) which will be used in theproposed method Its denition is introduced as follows
Table 1 Criteria for low-carbon supplier selection in the process of low-carbon building construction projects
Criteria Main criteria Subcriteria
Low-carbon supplier selection inthe process of low-carbon buildingconstruction projects
C1 low-carbon materials information
C11 materials costC12 low-carbon degree of materials
C13 materials qualityC14 materials exibility
C2 low-carbon business operation
C21 level of low-carbon information sharingC22 low-carbon logisticsC23 nancial capability
C24 emergency response capability
C3 potential for sustainable cooperationC31 desire of low-carbon cooperation
C32 enterprise reputationC33 low-carbon image
C4 low-carbon potentialC41 low-carbon certicationsC42 ecodesign of materials
C43 compatibility of low-carbon culture
C5 low-carbon technology capabilityC51 low-carbon production
Evaluating and selecting the bestlow carbon supplier
Calculating information contentsby IVTFIFWBM operator
Calculating attributeweight based on entropy-
TOPSIS
Calculating time weightbased on time degree and
ideal solution
Interval-valued triangular fuzzy multicriteriadecision-making model
Low carbon supplierselection criteria
Literaturereview
On-siteinvestigation
Policyanalysis
Project managers and experts evaluatealternative suppliers through interval-valued
triangular fuzzy numbers
Figure 1 Methodological framework for low-carbon supplier evaluation and selection
4 Advances in Civil Engineering
Definition 1 Let A as an intuitionistic fuzzy set (IFS)and A langx uA(x) vA(x)rang1113864 1113865x isin X with the conditionthat [45]
uA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
vA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
0le uA(x) + vA(x)le 1 x isin X
(1)
We can find that an IFS is constructed by twoinformation functions which not only describe themembership degree uA(x) but also describe the non-membership degree vA(x) Moreover the hesitancy in-formation of x isin X can be denoted by πA(x) 1minusuA(x)minus vA(x) which is called the hesitant index andtherefore IFS can describe the uncertainty and fuzzinessmore objectively than the usual fuzzy set
Definition 2 Zadeh first proposed the concept of triangularfuzzy number [43] Let X as a nonempty finite set A tri-angular fuzzy number intuitionistic fuzzy set (TFNIFS) A inX is defined as X langx 1113954uA(x) 1113954vA(x)rang|x isin X1113864 1113865 where 1113954uA
[1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] and 1113954vA [1113954vl
A(x) 1113954vmA (x) 1113954vu
A(x)] de-note respectively membership and nonmembership of theelement x in X to A and
0le 1113954uuA(x) + 1113954v
uA(x)le 1 1113954u
lA(x)ge 0 1113954v
lA(x)ge 0 (2)
en we call ([1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] [1113954vl
A(x) 1113954vmA (x)
1113954vuA(x)]) as an IVTFNIFN and it is also called as ([a
b c] [d e f]) [46]
Definition 3 Let 1113957α1 ([a1 b1 c1] [d1 e1 f1]) and 1113957α2
([a2 b2 c2] [d2 e2 f2]) are two random IVTFNIFN then
1113957α1 oplus 1113957α2 ( a1 + a2 minus a1a2 b1 + b2 minus b1b2 c1 + c2 minus c1c21113858 1113859
d1d2 e1e2 f1f21113858 11138591113857
(3)
1113957α1 otimes 1113957α2 1113874 a1a2 b1b2 c1c21113858 1113859 1113858d1 + d2 minus d1d2 e1 + e2 minus e1e2
Definition 4 For any IVTFNIFN 1113957α ([a b c] [d e f])the score of 1113957α can be evaluated by the score function S asfollows [47]
S(1113957α) a + 2b + c
4minus
d + 2e + f
4 (7)
where S(1113957α) isin [minus1 1]And an accuracy function is shown below
H(1113957α) a + 2b + c
42minus
a + 2b + c
4minus
d + 2e + f
41113888 1113889 (8)
Definition 5 Suppose 1113957α1 and 1113957α2 are two IVTFNIFN [48] where
(1) If S(1113957α1)≺ S(1113957α2) then 1113957α1 ≺ 1113957α2(2) If S(1113957α1) S(1113957α2) and when H(1113957α1)≺H(1113957α2) then
1113957α1 ≺ 1113957α2 when H(1113957α1) H(1113957α2) then 1113957α1 1113957α2
5 The Proposed Approach for Low-CarbonSuppliers Selection
51 Low-Carbon Suppliers Problem Description To thelow-carbon supplier selection problem in the process oflow-carbon building construction projects for which Si
S1 S2 Sm1113864 1113865(mge 2) is a discrete and feasible alterna-tive solution set of low-carbon suppliers Cj C11113864
C2 Cn(nge 2) is the finite set of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects w (w1 w2 wn)T is a weightvector which satisfies 0lewj le 1 1113936
nj1wj 1 and η(tk)
(η(t1) η(t2) η(tψ))T is the time weight vector where0le η(tk)le 1 and 1113936
ψk1η(tk) 1 e value of criteria Cj to
which solution Si is subject at moment tk is denoted asXij(tk) which is subject to an interval-valued triangularintuitionistic fuzzy denoted as Xij(tk) sim ηij(tk)
fij(tk)])mtimesn based on ψ moment of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Low-carbon supplier selectionproblems consist of multiple dimensions such as suppliercriteria and time Integration operator and determiningtime sequence weight are important technologies to re-duce dimensionality and solve low-carbon supplier se-lection problem under interval-valued intuitionistic fuzzyenvironment
52 Interval-Valued Triangular Fuzzy Number IntuitionisticFuzzy Bonferroni Means Operator
Definition 6 Let p qge 0 and ai(i 1 2 n) be a collec-tion of nonnegative numbers [48] If
Bpq
a1 a2 an( 1113857 1
n(nminus 1)1113944
n
ij1inej
api a
qj
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
1p+q
(9)
then Bpq is called the Bonferroni mean (BM)
Definition 7 Let 1113957αi ([ai bi ci] [di ei fi]) as a collection ofIVTFNIFNs For any p q≻0 if
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
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[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Definition 1 Let A as an intuitionistic fuzzy set (IFS)and A langx uA(x) vA(x)rang1113864 1113865x isin X with the conditionthat [45]
uA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
vA X⟶ [0 1] x isin X⟶ uA(x) isin [0 1]
0le uA(x) + vA(x)le 1 x isin X
(1)
We can find that an IFS is constructed by twoinformation functions which not only describe themembership degree uA(x) but also describe the non-membership degree vA(x) Moreover the hesitancy in-formation of x isin X can be denoted by πA(x) 1minusuA(x)minus vA(x) which is called the hesitant index andtherefore IFS can describe the uncertainty and fuzzinessmore objectively than the usual fuzzy set
Definition 2 Zadeh first proposed the concept of triangularfuzzy number [43] Let X as a nonempty finite set A tri-angular fuzzy number intuitionistic fuzzy set (TFNIFS) A inX is defined as X langx 1113954uA(x) 1113954vA(x)rang|x isin X1113864 1113865 where 1113954uA
[1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] and 1113954vA [1113954vl
A(x) 1113954vmA (x) 1113954vu
A(x)] de-note respectively membership and nonmembership of theelement x in X to A and
0le 1113954uuA(x) + 1113954v
uA(x)le 1 1113954u
lA(x)ge 0 1113954v
lA(x)ge 0 (2)
en we call ([1113954ulA(x) 1113954um
A (x) 1113954uuA(x)] [1113954vl
A(x) 1113954vmA (x)
1113954vuA(x)]) as an IVTFNIFN and it is also called as ([a
b c] [d e f]) [46]
Definition 3 Let 1113957α1 ([a1 b1 c1] [d1 e1 f1]) and 1113957α2
([a2 b2 c2] [d2 e2 f2]) are two random IVTFNIFN then
1113957α1 oplus 1113957α2 ( a1 + a2 minus a1a2 b1 + b2 minus b1b2 c1 + c2 minus c1c21113858 1113859
d1d2 e1e2 f1f21113858 11138591113857
(3)
1113957α1 otimes 1113957α2 1113874 a1a2 b1b2 c1c21113858 1113859 1113858d1 + d2 minus d1d2 e1 + e2 minus e1e2
Definition 4 For any IVTFNIFN 1113957α ([a b c] [d e f])the score of 1113957α can be evaluated by the score function S asfollows [47]
S(1113957α) a + 2b + c
4minus
d + 2e + f
4 (7)
where S(1113957α) isin [minus1 1]And an accuracy function is shown below
H(1113957α) a + 2b + c
42minus
a + 2b + c
4minus
d + 2e + f
41113888 1113889 (8)
Definition 5 Suppose 1113957α1 and 1113957α2 are two IVTFNIFN [48] where
(1) If S(1113957α1)≺ S(1113957α2) then 1113957α1 ≺ 1113957α2(2) If S(1113957α1) S(1113957α2) and when H(1113957α1)≺H(1113957α2) then
1113957α1 ≺ 1113957α2 when H(1113957α1) H(1113957α2) then 1113957α1 1113957α2
5 The Proposed Approach for Low-CarbonSuppliers Selection
51 Low-Carbon Suppliers Problem Description To thelow-carbon supplier selection problem in the process oflow-carbon building construction projects for which Si
S1 S2 Sm1113864 1113865(mge 2) is a discrete and feasible alterna-tive solution set of low-carbon suppliers Cj C11113864
C2 Cn(nge 2) is the finite set of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects w (w1 w2 wn)T is a weightvector which satisfies 0lewj le 1 1113936
nj1wj 1 and η(tk)
(η(t1) η(t2) η(tψ))T is the time weight vector where0le η(tk)le 1 and 1113936
ψk1η(tk) 1 e value of criteria Cj to
which solution Si is subject at moment tk is denoted asXij(tk) which is subject to an interval-valued triangularintuitionistic fuzzy denoted as Xij(tk) sim ηij(tk)
fij(tk)])mtimesn based on ψ moment of criteria for low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Low-carbon supplier selectionproblems consist of multiple dimensions such as suppliercriteria and time Integration operator and determiningtime sequence weight are important technologies to re-duce dimensionality and solve low-carbon supplier se-lection problem under interval-valued intuitionistic fuzzyenvironment
52 Interval-Valued Triangular Fuzzy Number IntuitionisticFuzzy Bonferroni Means Operator
Definition 6 Let p qge 0 and ai(i 1 2 n) be a collec-tion of nonnegative numbers [48] If
Bpq
a1 a2 an( 1113857 1
n(nminus 1)1113944
n
ij1inej
api a
qj
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
1p+q
(9)
then Bpq is called the Bonferroni mean (BM)
Definition 7 Let 1113957αi ([ai bi ci] [di ei fi]) as a collection ofIVTFNIFNs For any p q≻0 if
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
(3) Monotonicity let 1113957αi ([ai bi ci] [di ei fi])(i
1 2 n) and 1113957αΔi ([1113954αi1113954bi 1113954ci] [1113954di 1113954ei
1113954fi]) are twopositive collections of IVTFNIFN if ai ge 1113954αi bi ge1113954bi ci ge1113954ci di le 1113954di ei le 1113954ei fi le 1113954fi for all i then
(4) Boundedness let 1113957αi ([ai bi ci] [di ei fi])(i 1
2 n) as a positive collection of IVTFNIFN then
1113957αminus le IVTFNIFBMpq1113957α1 1113957α2 1113957αn( 1113857le 1113957α+
1113957αminus min aii
min bii
min cii
1113890 1113891 min dii
min eii
minfii
1113890 11138911113888 1113889
1113957α+ max ai
i
max bii
max cii
1113890 1113891 max dii
max eii
maxfii
1113890 11138911113888 1113889
(27)
e TFNIFWBM considers the interaction betweencriteria for low-carbon supplier selection in the processof low-carbon building construction projects but theyhave different levels of importance in low-carbon sup-plier selection erefore we first propose IVTFNIFBMoperator
Advances in Civil Engineering 9
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
In the aforementioned analysis we consider the attributeinterrelationships which are important However in manypractical situations we should take into account the weightsof the data So we first define an IVTFNIFBM operator
Definition 8 Let 1113957αi ([ai bi ci] [di ei fi]) as a posi-tive collection of IVTFNIFN w (w1 w2 wn)T is theweight vector of 1113957αi(i 1 2 n) where wi ge 0 and1113936
eorem 2 can be proved by mathematical induction ina similar way we can prove that IVTFNIFWBM operator alsohas idempotency commutativity monotonicity and bounded-ness features and the detailed proof procedures are omitted here
53 Time Weight Based on Time Degree and Ideal Solution
Definition 9 Supposing η(tk) (η(t1) η(t2) η(tk))T
represents time sequence weight vector where η(tk) rep-resents the weight of kth time period and η(tk) isin [0 1]1113936
ψk1η(tk) 1 time sequence weight indicates the attention-
attaching degree on different time periods in decision-making process
Information entropy can reflect the uptake degree oftime weight vector against information quantity the greaterthe entropy is the less the information quantity it containserefore based on maximum entropy principle we solvethe time weight of time degree and information entropy andset up a nonlinear programming model as follows
max I minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1]
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(31)
When λ gets closer to 0 indicating decision-maker at-taches more preference to recent information of time serieswhen λ gets closer to 1 indicating decision-maker attachesmore preference to forward information of time series Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Definition 10 Based on the Definition 8 when we considerthe equilibrium of time preference of decision makers indifferent time periods we can determine time weight basedon an objective function of maximization closeness degree toideal solution with subjective time preference We denoteη(tk)+ as positive ideal time weight and negative ideal timeweight is denoted by η(tk)minus
Let the distance between the two time weight vectorsη( 1113957tk) (η( 1113957t1)η( 1113957t2) η( 1113957tψ))T and η( 1113954tk) (η( 1113954t1)η( 1113954t2)
η( 1113954tψ))T be
d η 1113957tk( 1113857 η 1113954tk( 1113857( 1113857
1113944
ψ
k1η 1113957tk( 1113857minus η 1113954tk( 1113857( 1113857
2
11139741113972
(32)
en the distances between a time weight vector η(tk)
(η(t1) η(t2) η(tk))T and positive and negative idealtime weight vectors respectively are
10 Advances in Civil Engineering
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
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Submit your manuscripts atwwwhindawicom
d η tk( 1113857 η tk( 1113857+
( 1113857
1113944
ψminus1
k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
2
11139741113972
d η tk( 1113857 η tk( 1113857minus
( 1113857
1minus η t1( 1113857( 11138572
+ 1113944
ψ
k2η tk( 1113857
2
11139741113972
(33)
e relative closeness degree between time weight vectorη(tk) and ideal time weight vector η(tk)+ can be obtained
c η tk( 1113857 η tk( 1113857+
( 1113857 d η tk( 1113857 η tk( 1113857
minus( 1113857
d η tk( 1113857 η tk( 1113857+
( 1113857 + d η tk( 1113857 η tk( 1113857minus
( 1113857
(34)
en based on time degree and ideal solution con-structing a nonlinear programming model is as follows
max c η tk( 1113857 η tk( 1113857+
( 1113857
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎩
(35)
Based on the thought of ldquostress the present rather thanthe pastrdquo the more recent information can fully reflect thecharacteristics of decision-making attributes and it wouldbe more effective for decision-making evaluation results Wesolve this model by Lingo11 software and acquire the timesequence weight vector
Based on (31) and (35) this paper constructs a com-prehensive time weight while considering the uptakeability of time weight against information as well as theeffectiveness of recent decision-making information asfollows
max R l
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
1minus η t1( 1113857( 11138572
+ 1113936ψk2η tk( 1113857
21113969
+
1113936ψminus1k1η tk( 1113857
2+ 1minus η tψ1113872 11138731113872 1113873
21113969 +(1minus l) minus1113944
ψ
k1η tk( 1113857ln η tk( 1113857⎛⎝ ⎞⎠
st λ 1113944
ψ
k1
ψ minus k
ψ minus 1η tk( 1113857 1113944
ψ
k1η tk( 1113857 1 η tk( 1113857 isin [0 1] k 1 2 ψ
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎩
(36)
where l is an adjustable coefficient l isin [0 1] if l is close to 0it is the sign that decision makers are more inclined to thetime weight based on objective information-driven andwhen the l is close to 1 the decision makers are moreemphasized on time weight based on subjective preferenceinformation We also solve this model by Lingo11 softwareand acquire the time sequence weight vector
54 e Weight of Attribute Based on Entropy-TOPSIS
Definition 11 Let 1113957α (ai bi ci) and 1113957β (1113954ai1113954bi 1113954ci) are two
collections of IVTFNIFNs then the distances between 1113957αand 1113957β is
D(1113957α 1113957β)
13
ai minus 1113954ai( 11138572
+ bi minus 1113954bi1113872 11138732
+ ci minus1113954ci( 11138572
1113876 1113877
1113970
(37)
Based on the decision-making situations of uncertaintymulticriteria and finite case we let 1113957A (A1 A2 An) asn alternatives 1113957C (C1 C2 Cn) as a collection of attri-butes w (w1 w2 wn)T is the weight vector of 1113957C wherewi ge 0 and 1113936
ni1wi 1
If the performance of the alternative Ai with respect tothe attributes Cj is measured by an IVTFNIFNs allIVTFNIFNs are contained in an intuitionistic fuzzy decisionD (1113958dij)ntimesm
Definition 12 If dlowastj (1113957dj1113954dj d
j) is an ideal performancevalues of attributes there are generally benefit criteria andcost criteria
When the performance values of the benefit typethen 1113957dj max
i
1113957dij 1113954dj maxi
1113954dij d
j maxi
d
ijWhen the performance values of the cost type then
1113957dj mini
1113957dij 1113954dj mini
1113954dij d
j mini
d
ijIn general the alternatives have a small difference in the
performance value of attributes namely the attributes havea small influence on a multiple attribute decision-makingproblem Conversely the more the difference the more theeffect erefore the larger the performance value of at-tributes deviation the larger the attributes weight We canlearn from the entropy that the lower the entropy is themore the information quantity it contains
Due to the limit of entropy we need to acquire stan-dardized decision-making matrix by (37) and get a distancebetween the attributes and the ideal attributes
Advances in Civil Engineering 11
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Steps of the weight of attribute are provided as followsFirst constructing the ideal performance values of at-
tributes by Definition 11 based on the IVTFNIFN Nextcalculating the distance from each attributes and ideal at-tributes via Formula (37) en we can construct a distancematrix R1 (1113957rij)ntimesm R2 (1113954rij)ntimesm where we userlowastij rij1113936
mi1rij then conduct standardization on IVTF-
NIFN distance matrix Rlowast1 (1113957rlowastij)ntimesm and Rlowast2 (1113954rlowastij)ntimesm Fi-nally calculating the weight of attributes1113957C (C1 C2 Cn)
ej minus1113944n
i1rlowastij times ln r
lowastij1113872 1113873ln n
w1j
1minus e1j
1113936mj1 1minus e1j1113872 1113873
(j 1 2 m)
w2j
1minus e2j
1113936mj1 1minus e2j1113872 1113873
(j 1 2 m)
wj w1
jw2j
1113969(j 1 2 m)
(38)
We can know the final comprehensive weightwj(j 1 2 3 m)
55 Steps of Low-Carbon Supplier Selection in the Process ofLow-Carbon Building Construction Projects Accordingto the calculation process of the above model for low-carbon supplier selection in the process of low-carbonbuilding construction projects the calculation steps are asfollows
Step 1 e original information matrix DXij(tk) ([aij(tk)
bij(tk) cij(tk)] [dij(tk) eij(tk) fij(tk)])mtimesn of low-carbonsupplier selection is given by our project collaborators whoare construction project managers practitioners and in-dustry experts based on the different ψ moments
Step 2 Based on the main criteria of low-carbon supplierselection for constructor in Table 1 we form informationmatrix for criteria and calculate the criteria weight set w
(w1 w2 wn)T according to Formulas (37) and (38)en we calculate the time sequence weight set η(tk)
(η(t1) η(t2) η(tψ))T according to Formula (36) bysolving the model via Lingo 110 software
Step 3 Utilizing the IVTFIFWBM operator to aggregatethe criteria information of low-carbon supplier selectionbased on the criteria weight which is calculated in Step 2en we need to aggregate all individual criteria in-formation Cj potential low-carbon suppliers into a col-lective criteria information matrix DXij(tk)
prime ([aijprime (tk)
bijprime (tk) cijprime (tk)] [dij
prime (tk) eijprime (tk) fij
prime (tk)])mtimesn according toFormula (23)
Step 4 Gathering the information of time dimension of low-carbon supplier selection based on the time sequence weight
set η(tk) (η(t1) η(t2) η(tψ))T en we create thecomprehensive decision information matrix DPrimeXi
([aPrimei
bPrimei cPrimei ] [dPrimei ePrimei fPrimei ])mtimes1 via Formula (29) for the single di-mension to potential low-carbon suppliers Si
Step 5 Finally selecting the best low-carbon supplier in theprocess of low-carbon building construction projectsbased on ranking value Li (L1 L2 Li) and furtherdetermining the priority sequence of low-carbon supplierSi(i 1 2 m)
6 Case Study
61 Case Company Background According to the aboveanalysis the proposed method is applied on the case of thehousing construction project entity in the constructionindustry to solve low-carbon supplier selection problem
Company HFG founded in 1986 is a builder enterprisewhich has special qualifications for construction located inTai Yuan a city of Shan Xi Province in China HFGrsquosbusiness scope involves housing construction general con-tracting infrastructure construction real estate investmentengineering design and other fields in the major cities HFGwill be committed to green housing technology developmentand practice with product innovation and the provision oflow-carbon building products as the development goal Forbuilder HFG one of the important issues is how to reducecarbon emissions of construction projects to enhance low-carbon competitiveness and profit In this circumstancesHFG needs to select its low-carbon supplier from a largenumber of suppliers in the process of low-carbon buildingconstruction projects
As builder HFG has some experience accumulation inthe supplier selection it is still a difficult problem forHFG toselect its best low-carbon supplier from these potentialsuppliers in the process of low-carbon building constructionprojects On the one hand builder H has established a cri-terion which is not appropriate to use it to select low-carbonsupplier It did not establish the criteria for the low-carbonsupplier selection in the process of low-carbon buildingconstruction projects On the other hand builder HFG notonly has to nondimensionalize the criteria to previoussupplier selection but alsomore focus on the single period ofdecision criteria information and even if HFG considersmultiple timings during supplier selection it may still lead tosubjectivity and objectivity in the time weight Moreover theselection method is very difficult for builder HFG to dealwith qualitative criteria in the process of low-carbon supplierselection
62 Application of the Proposed Criteria and Method Tobuilder HFG the proposed criteria and method is suitableto be used to select low-carbon supplier in the process oflow-carbon building construction projects because themanagers and practitionerrsquos understanding of the weightsof criteria for low-carbon supplier selection is in the fuzzystate in builder HFG In addition expert scoring methodwhich is usually used to select traditional supplier in their
12 Advances in Civil Engineering
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
construction projects makes the proposed criteria andmethod more realistic and practical
For the moment builder HFG is required to purchasea batch of rebar for a low-carbon building in Tai Yuan Afterthe primary selection of steel production enterprises thereare four enterprises Si S1 S2 S3 S41113864 1113865 to enter the finalselection Builder H needs to select its steel supplier from 4main low-carbon suppliers by the proposed criteria andmethod erefore Hrsquos 15 managers practitioners andexperts are asked to determine the criteria of low-carbonsupplier selection to construction projects based on thepreliminary list of criteria compiled including literaturereview about low-carbon supplier selection and the builderHrsquos actual situation It can be seen in Table 1 including 5main criteria and 17 subcriteria Moreover they select thetime sequence set of different historical periods for nearlythree years tk (t1 t2 t3) for the previously mentionedpotential low-carbon suppliers For the sake of simplicity weonly give out the calculation for the 5 main criteria eevaluated values of 4 main suppliers which are given by 15managers practitioners and experts are listed in Tables 2ndash4
Based on the original evaluation criteria informationmatrix of low-carbon supplier selection which only includessupplier S1 supplier S2 supplier S3 and supplier S4 in theprocess of low-carbon building construction projects perStep 2 according to Formulas (37) and (38) the criteriaweight is shown in Table 5 e time degree parameterλ 03 and the discrete time weight vector is solved viaStep 2 and Lingo 110 software η(tk) (η(t1) η(t2)
η(t3))T (0582 0236 0182)
Based on the criteria weight vector w (w1 w2 w3
w4 w5) per Step 3 the five criteria were assembled intoa collective the criteria information of low-carbon supplierselection matrix from 3 periods of time Comprehensivecriteria making information of each potential low-carbonsuppliers were assembled from different moment per Step4 forming comprehensive selection information matrix forthe target single dimension in the end the value of eachpotentiallow-carbon suppliers for the construction projectwas determined based on Step 5 and is shown in Tables 6ndash8
us the low-carbon supplier who will provide thebatch of rebar for the low-carbon building in Tai Yuan isdetermined to S1 Based on the evaluation and selectionabove supplier S1 is recommended as builder HFGrsquos bestlow-carbon supplier In fact builder HFG has given priorityto supplier S1 who provides the batch of rebar for the low-carbon building in Tai Yuan according to the results In
addition supplier S3 is recommended as the reserved low-carbon supplier HFGrsquos low-carbon housing technologydevelopment and practice will improve its competitivenessand profitability in the construction industry based on theconcept of continuous improvement
7 Conclusions
ere has been broad consensus on carbon emissions re-duction around the world Low-carbon building not onlycan bring a healthier and more comfortable living envi-ronment but also can reduce carbon emissions in theconstruction industry For constructors using low-carbonbuilding materials for construction and sustainable devel-opment of the environment is particularly importantIn addition GSCM has become an inevitable choice forconstructors to cope with the pressure from the governmentand the market erefore it is one of the most importantfactors to select low-carbon supplier in the process of low-carbon building construction projects
In this paper we propose a dynamic multiattributedecision-making approach with interval-valued triangularfuzzy numbers intuitionistic fuzzy for low-carbon supplierselection in the process of low-carbon building constructionprojects According to the demand of constructors in theprocess of low-carbon building construction projects 5main criteria and 17 subcriteria are established for low-carbon supplier selection in the construction industry eproposed method considers interaction between criteria oflow-carbon supplier selection and the influence of con-structorsrsquo subjective preference and objective criteria in-formation e evaluated values of potential low-carbonsuppliers are given by managers practitioners and expertse proposed criteria andmethod are suitable to use to selectlow-carbon supplier in the process of low-carbon buildingconstruction projects because the managers and practi-tionerrsquos understanding of the weights of criteria for low-carbon supplier selection are in the intuitionistic fuzzy dueto the nature of unquantifiable and incomplete informationin low-carbon supplier selection In addition expert scoringmethod which is usually used to select traditional supplier intheir construction projects makes the proposed criteria andmethod more realistic and practical e proposed criteriaand method have been successfully implemented in a caseconstruction project to select the best low-carbon supplier Itnot only is much easier for constructors to select low-carbonsupplier but also can make the localization of low-carbon
Table 2 Original evaluation criteria information matrix at the moment t1
C1 C2 C3 C4 C5
S1([060708][010203])
([050606][020202])
([010104][020205])
([060707][010203])
([070809][010101])
S2([020304][040505])
([040405][040405])
([010202][060708])
([030405][020203])
([050607][020203])
S3([040506][010202])
([030405][030404])
([020304][050606])
([060708][010202])
([070707][010202])
S4([060607][020202])
([040506][020203])
([060607][010101])
([040505][010203])
([020304][050606])
Advances in Civil Engineering 13
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
supplier more practical and more accurate in the con-struction industry Finally low-carbon supplier selection ofbuilderHFG for a low-carbon building in Tai Yuan is studiedto verify the scientificity and feasibility of the proposedcriteria and method e result shows that this criteria andmethod are of effectiveness and practicality of low-carbonsupplier selection in the process of low-carbon buildingconstruction projects Also it can be mentioned that the
proposed model can be easily extended to analyze othermanagement decision problems as a structural model
is study has some limitations that warrant future re-search attention e attribute weight method based on theEntropy-TOPSIS model in this paper is only an objective as-signment method A comprehensive attribute weight methodconsidering the objective assignment information and sub-jective preferences of decision makers should be studied in thefuture Moreover evaluation criteria information cannot be
Table 3 Original evaluation criteria information matrix at the moment t2
C1 C2 C3 C4 C5
S1([020304][030404])
([050607][020202])
([050506][010205])
([060707][010203])
([040506][010101])
S2([030405][010203])
([040505][010202])
([030405][010203])
([040506][020203])
([060607][010202])
S3([040506][010202])
([070707][010101])
([040505][010203])
([060708][010202])
([030405][020303])
S4([060607][010101])
([040506][020203])
([060607][010101])
([020303][030405])
([020304][050606])
Table 4 Original evaluation criteria information matrix at the moment t3
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
effectively reflected by using IVTFNs under uncertain linguisticenvironment For further study we will extend the proposedmethod in this paper with linguistic intuitionistic fuzzy numberand prospect theory in other civil engineering fields
Data Availability
All data generated or analyzed to support the findings of thisstudy are included within the article
Conflicts of Interest
e authors declare that they have no conflicts of interest
Acknowledgments
e authors would like to thank Min Yan is research wassupported by the National Natural Science Foundationof China (71473055) the Fundamental Research SpecialFunds for the Central Universities (HEUCFW170912HEUCFP201824) the Humanities and Social Sciences Foun-dation of Ministry of Education of China (14YJA630002) theNational Natural Science Foundation of China (71804084) theHumanities and Social Sciences Foundation of Ministry ofEducation of China (15YJC630162) the Humanities and SocialSciences Foundation of Ministry of Education of China(18YJC630245) the China Postdoctoral Science FoundationFunded Project (2017M620814) and the National Social Sci-ence Foundation of China (17BGL238)
References
[1] J Yudelson Green Building A to Z Understanding the Lan-guage of Green Building New Society Publishers GabriolaIsland BC Canada 2007
[2] IPOC Climate Change 2014 Synthesis Report EnvironmentalPolicy Collection vol 27 no 2 p 408 2014
[3] B Kang Y Hu Y Deng and D Zhou ldquoA new methodologyof multicriteria decision-making in supplier selection basedon Z-numbersrdquo Mathematical Problems in Engineeringvol 2016 no 1 pp 1ndash17 2016
[4] A H I Lee H Y Kang C F Hsu and H C Hung ldquoA greensupplier selection model for high-tech industryrdquo ExpertSystems with Applications vol 36 no 4 pp 7917ndash7927 2009
[5] C W Hsu T C Kuo S H Chen and A H Hu ldquoUsingDEMATEL to develop a carbon management model ofsupplier selection in green supply chain managementrdquoJournal of Cleaner Production vol 56 no 10 pp 164ndash1722013
[6] D Kannan and C J C Jabbour ldquoSelecting green suppliersbased on GSCM practices Using fuzzy TOPSIS applied toa Brazilian electronics companyrdquo European Journal of Op-erational Research vol 233 no 2 pp 432ndash447 2014
[7] C W Tsui and U P Wen ldquoA hybrid multiple criteria groupdecision-making approach for green supplier selection in theTFT-LCD industryrdquo Mathematical Problems in Engineeringvol 2014 Article ID 709872 13 pages 2014
[8] O Gurel A Z Acar I Onden and I Gumus ldquoDeterminantsof the green supplier selectionrdquo Procedia-Social and Behav-ioral Sciences vol 181 no 4 pp 131ndash139 2015
[9] H MW Chen S Y Chou Q D Luu and H K Yu ldquoA fuzzyMCDM approach for green supplier selection from the
economic and environmental aspectsrdquo Mathematical Prob-lems in Engineering vol 2016 Article ID 8097386 10 pages2016
[10] F Yu Y Yang D Chang F Yu and Y Yang ldquoCarbonfootprint based green supplier selection under dynamic en-vironmentrdquo Journal of Cleaner Production vol 170 no 8pp 880ndash889 2017
[11] K Govindan and R Sivakumar ldquoGreen supplier selectionand order allocation in a low-carbon paper industry in-tegrated multi-criteria heterogeneous decision-making andmulti-objective linear programming approachesrdquo Annals ofOperations Research vol 238 no 3 pp 243ndash276 2016
[12] Q Pang T Yang M Li and Y Shen ldquoA fuzzy-grey multi-criteria decision making approach for green supplier selectionin low-carbon supply chainrdquo Mathematical Problems inEngineering vol 1 pp 1ndash9 2017
[13] A P C Chan A Darko and E A Effah ldquoStrategies forpromoting green building technologies adoption in theconstruction industrymdashAn international studyrdquo Sustain-ability vol 9 no 6 p 969 2017
[14] K Govindan R Khodaverdi and A Jafarian ldquoA fuzzy multicriteria approach for measuring sustainability performance ofa supplier based on triple bottom line approachrdquo Journal ofCleaner Production vol 47 no 47 pp 345ndash354 2013
[15] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision-making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical Problems in Engineering vol 2017 Article ID7954784 13 pages 2017
[16] S Darabi and J Heydari ldquoAn interval- valued hesitant fuzzyranking method based on group decision analysis for greensupplier selectionrdquo IFAC-Papers On Line vol 49 no 2pp 12ndash14 2016
[17] W C Yeh and M C Chuang ldquoUsing multi-objective geneticalgorithm for partner selection in green supply chain prob-lemsrdquo Expert Systems with Applications vol 38 no 4pp 4244ndash4253 2011
[18] A Kumar V Jain S Kumar and C Chandra ldquoGreen supplierselection a new geneticimmune strategy with industrialapplicationrdquo Enterprise Information Systems vol 10 no 8pp 911ndash943 2015
[19] M Gupta ldquoSupplier selection using artificial neural networkand genetic algorithmrdquo International Journal of IndianCulture and Business Management vol 11 no 4 pp 457ndash4722015
[20] M Punniyamoorthy P Mathiyalagan and P Parthiban ldquoAstrategic model using structural equation modeling and fuzzylogic in supplier selectionrdquo Expert Systems with Applicationsvol 38 no 1 pp 458ndash474 2011
[21] A Fallahpour E U Olugu S N Musa D Khezrimotlaghand K Y Wong ldquoAn integrated model for green supplierselection under fuzzy environment application of data en-velopment analysis and genetic programming approachrdquoNeural Computing and Applications vol 27 no 3 pp 707ndash725 2016
[22] L H Li J C Hang Y Gao and C Y Mu ldquoUsing an in-tegrated group decision method Based on SVM TFN-RS-AHP and TOPSIS-CD for cloud service supplier selectionrdquoMathematical Problems in Engineering vol 3 pp 1ndash14 2017
[23] Z Hu C Rao Y Zheng and D Huang ldquoOptimization de-cision of supplier selection in green procurement under themode of low carbon economyrdquo International Journal ofComputational Intelligence Systems vol 8 no 3 pp 407ndash4212015
Advances in Civil Engineering 15
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[24] J Qin X Liu and W Pedrycz ldquoAn extended TODIM multi-criteria group decision making method for green supplierselection in interval type-2 fuzzy environmentrdquo EuropeanJournal of Operational Research vol 258 no 4 pp 626ndash6382017
[25] P Ghadimi A Dargi and C Heavey ldquoSustainable supplierperformance scoring using audition check-list based fuzzyinference system a case application in automotive spare partindustryrdquo Computers and Industrial Engineering vol 105no 2 pp 12ndash27 2017
[26] R R Yager ldquoOn generalized Bonferroni mean operators formulti-criteria aggregationrdquo International Journal of Approx-imate Reasoning vol 50 no 8 pp 1279ndash1286 2009
[27] Z S Xu ldquoIntuitionistic fuzzy Bonferroni meansrdquo IEEETransactions on Systems Man and Cybernetics-Part B Cy-bernetics vol 41 no 2 pp 568ndash578 2011
[28] M Xia Z Xu and B Zhu ldquoGeneralized intuitionistic fuzzyBonferroni meansrdquo International Journal of Intelligent Sys-tems vol 27 no 1 pp 23ndash47 2011
[29] W Zhou and J M He ldquoIntuitionistic fuzzy geometricBonferroni means and their application in multicriteria de-cision makingrdquo International Journal of Intelligent Systemsvol 27 no 12 pp 995ndash1019 2012
[30] B Zhu ldquoHesitant fuzzy geometric Bonferroni meansrdquo In-formation Science vol 205 no 1 pp 72ndash85 2012
[31] P D Liu L L Zhang X Liu and P Wang ldquoMulti-valuedneutrosophic number Bonferroni mean operators with theirapplications in multiple attribute group decision makingrdquoInternational Journal of Information Technology amp DecisionMaking vol 15 no 5 pp 1181ndash1210 2016
[32] X Liu Z Tao H Chen and L Zhou ldquoA new interval-valued2-tuple linguistic bonferroni mean operator and its app-lication to multi-attribute group decision makingrdquoInternational Journal of Fuzzy Systems vol 19 no 1pp 86ndash108 2017
[33] G W Wei ldquoSome geometric aggregation functions and theirapplication to dynamic multiple attribute decision making inthe intuitionistic fuzzy settingrdquo International Journal ofUncertainty Fuzziness and Knowledge-Based Systems vol 17no 2 pp 179ndash196 2011
[34] J H Park H J Cho and Y C Kwun ldquoExtension of theVIKOR method to dynamic intuitionistic fuzzy multiple at-tribute decision makingrdquo Computers and Mathematics withApplications vol 65 no 4 pp 731ndash744 2013
[35] S Yin B Li H Dong and Z Xing ldquoA new dynamic mul-ticriteria decision making approach for green supplier se-lection in construction projects under time sequencerdquoMathematical problems in Engineering vol 2 pp 1ndash13 2017
[36] Z S Xu ldquoOn multi-period multi-attribute decisionmakingrdquo Knowledge-Based Systems vol 21 no 2pp 164ndash171 2008
[37] Z S Xu and J Chen ldquoBinomial distribution based approachto deriving time series weightsrdquo in IEEE International Con-ference on Industrial Engineering and Engineering Manage-ment pp 154ndash158 Bangkok ailand 2007
[38] P Liu and F Teng ldquoMultiple criteria decision making methodbased on normal interval-valued intuitionistic fuzzy gener-alized aggregation operatorrdquo Complexity vol 21 no 5pp 277ndash290 2016
[39] R Sadiq and S Tesfamariam ldquoProbability density functionsbased weights for ordered weighted averaging (OWA) op-erators an example of water quality indicesrdquo EuropeanJournal of Operational Research vol 183 no 3 pp 1350ndash13652007
[40] X Z Zhang and C X Zhu ldquoGeneralized precedence ordermethod with ranking preference for multi-attribute decisionmakingrdquo Systems Engineering-eory and Practice vol 33no 11 pp 2852ndash2858 2013
[41] B Sun and X F Xu ldquoA dynamic stochastic decision-makingmethod based on discrete time sequencesrdquo Knowledge-BasedSystems vol 105 no 4 pp 23ndash28 2016
[42] G W Wei ldquoTwo-tuple linguistic multiple attribute groupdecision making with incomplete attribute weight in-formationrdquo Systems Engineering and Electronics vol 30 no 2pp 273ndash277 2008
[43] Z S Chen and Y S Li ldquoApproach for normal triangular fuzzystochastic multiple attribute decision making based onprospect mean-variance rulerdquo Control and Decision vol 29no 7 pp 1239ndash1249 2014
[44] YMWang C P Que and Y X Lan ldquoHesitant fuzzy TOPSISmulti-attribute decision method based on prospect theoryrdquoControl and Decision vol 32 no 5 pp 864ndash870 2017
[45] K T Atanassov ldquoIntuitionistic fuzzy setsrdquo Fuzzy Sets andSystems vol 20 pp 87ndash96 1986
[46] Z S Xu and Q Chen ldquoA multi-attribute decision-makingprocess based on interval-valued intuitionistic fuzzy Bon-ferroni meanrdquo Journal of Systems Engineering and Electronicsvol 20 no 2 pp 217ndash228 2011
[47] X F Wang ldquoFuzzy number intuitionistic fuzzy geometricaggregation operators and their application to decisionmakingrdquo Control and Decision vol 23 no 6 pp 607ndash6122008
[48] C Bonferroni ldquoSulle medie multiple di potenzerdquo BolletinoMatematica Italiana vol 5 pp 267ndash270 1950
