rticle history:eceived 21 August 2015eceived in revised form 19 January 2016ccepted 13 April 2016vailable online xxx
eywords:FD
a b s t r a c t
Computer workstation selection is a multiple criteria decision making problem that is generally basedon vague linguistic assessments, which represent human judgments and their hesitancy. In this paper,a new fuzzy quality function deployment (QFD) approach is used to effectively determine the designrequirements (DRs) of a computer workstation. Hesitant fuzzy linguistic term sets (HFLTS) are innova-tively employed to capture the hesitancy of the experts in this approach. More precisely, the proposednew QFD approach is the first study that determines the importance of customer requirements (CRs),the relations between CRs and DRs and the correlations among DRs via HFLTS. Additionally, HFLTS based
esitant fuzzy setsFLTSorkstation
esign requirementustomer requirementsOPSIS
Analytic Hierarchy Process (AHP) and Technique for Order Performance by Similarity to Ideal Solution(TOPSIS) methods are utilized in the computational steps to select the best computer workstation. A realindustrial application is carried out to validate the implementation of the proposed approach.
A workstation is a customized computer that is designed forpecific scientific or technical application. Increasing competitionnd technological innovation in the industry and business world ineneral brings about new developments in the workstation design.owever, workstations are usually designed arbitrarily with lit-
le consideration to the specific needs and requirements of theirsers. Considering additional benefits of tailor-made workstationshat are customized for specific uses and needs, a customer-drivenpproach in workstation design would benefit companies. Such anpproach would not only capture customers’ perspectives, but alsoaise the overall level of their satisfaction level. Quality functioneployment (QFD) is a customer-driven tool that is widely used
or product planning purposes. It can be beneficial to reach higherevels in customer satisfaction [1,2]. Good design requires consider-tion of design aspects that clients want and expect. To address this,FD uses a matrix called House of Quality (HOQ) [3] that translates
Please cite this article in press as: S. Cevik Onar, et al., A new hesitanselection, Appl. Soft Comput. J. (2016), http://dx.doi.org/10.1016/j.aso
ustomer Needs or Requirements (CRs) into engineering character-stics or Design Requirements (DRs). The HOQ is constructed withhe importance weights of each of the CRs, as well as the correla-
tion matrix among DRs and the relationship matrix between CRsand DRs [1–5].
The importance levels of CRs, functional relationships amongCRs and DRs, and the assessments of alternatives based on DRsare difficult to express precisely. Although crisp data are needed todesign workstations, experts usually prefer to provide their evalu-ations in linguistic terms. The fuzzy set theory lets these linguisticassessments be incorporated into numerical analyses. The ordi-nary fuzzy sets have been recently extended to Type 2 fuzzy sets,hesitant fuzzy sets, intuitionistic fuzzy sets, non-stationary fuzzysets and fuzzy multisets [6]. Hesitant fuzzy sets (HFS), which aredeveloped by Torra [7], allow more than one value for defining themembership value of an element, enabling an expert better expresshis/her assessment [8]. In this paper, we prefer to use hesitant lin-guistic term sets (HFLTS) in the development of a new fuzzy QFDapproach since HFLTS enable the integration of various linguisticevaluations assigned by experts as an inclusive linguistic interval.HFLTS have been used in several papers in the literature [9–16].
Main features of the proposed hesitant fuzzy QFD approachare its use of HFLTS in the pairwise comparisons among CRs,relations between CRs and DRs, correlations among DRs and eval-
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
uation of alternatives. The weights of the CRs are determined bya hierarchical and pairwise comparison-based approach while thealternatives are ranked by using a hesitant fuzzy TOPSIS method.Besides, we propose a new approach taking the hesitant correla-
ions among DRs into account in the HOQ operations. To the best ofur knowledge, there is no QFD study based on hesitant fuzzy sets
n the literature and this study is different from the other existingpproaches since it considers the experts’ hesitancies in each phasef the QFD approach.
The remainder of this paper is structured as the following; Sec-ion 2 presents basic concepts of QFD and a literature review ofuzzy QFD methodology. In Section 3, the main concepts of HFSnd HFTLS are given. Section 4 gives the proposed decision mak-ng approach which is based on hesitant fuzzy QFD. In Section 5, aase study is provided to demonstrate the applicability of the pro-osed method. The last section concludes the paper and gives someerspectives.
. Literature survey on fuzzy QFD
The overall methodological structure is based on the QFD tech-ique, supported by a hesitant fuzzy set approach, where linguisticata are considered. In the following, first, basic QFD terminologyn classical QFD is given. Then a literature review on fuzzy setxtensions in QFD is given.
.1. Quality function deployment (QFD)
QFD is a popular quality method that is developed in the 1960snd 1970s to address design quality challenges to meet betterustomer expectations [1,2]. QFD is a proven and comprehensiveechnique that is able to translate CRs into DRs by the so-called isOQ [3]. The HOQ is the basic structure of QFD and includes the fol-
owing integral components: the relationship matrix between CRsnd DRs, CRs’ importance weights, and the correlation matrix forRs [1–5]. The well-known HOQ approach is depicted in Fig. 1.
The integral elements of the typical HOQ structure shown inig. 1 are briefly introduced below:
CRs: Customer requirements are also known as customerttributes, customer needs or demanded quality. The first step foronstructing an HOQ is the identification, clarification and speci-cation of customer needs. CRs represent the initial input for theOQ and highlight those product specifications that should be paidttention to so that the “voice of the customer” is well understood.
DRs: Design requirements are also called product features, engi-eering attributes, technical attributes, engineering characteristicsr substitute quality characteristics. These product requirementsre associated with CRs.
CRs’ analysis: Not all of CRs have the same level of importanceor customers. In order to prioritize the identified CRs, a directvaluation or different analytical techniques can be adopted.
Relationships matrix between CRs and DRs: The relationshipatrix represents the extent to which each DR affects its associated
R. This matrix constitutes the body of the HOQ.DRs’ analysis: The results taken from the previous steps are used
o compute the final importance degrees of DRs.The HOQ is frequently discussed and applied in theoretical and
ractical literature, as it has the potential to significantly improvehe accuracy of the preceding steps. HOQ is oriented towards designnd is thus an important resource for designers. Furthermore, it is
tool that can summarize customers’ feedback and translate it into useful information format that can be easily understood and usedy design teams.
Companies can enjoy various advantages when applying QFD,s it is customer-oriented, helps to combine large amount of
Please cite this article in press as: S. C evik Onar, et al., A new hesitanselection, Appl. Soft Comput. J. (2016), http://dx.doi.org/10.1016/j.aso
erbal data, brings multifunctional teams together, improves theonsensus processes, creates competitive advantage, decreasestart-up and engineering costs borne during product developmentrocesses, and is usable across a wide range of processes and ser-
PRESSmputing xxx (2016) xxx–xxx
vices in different sectors [1–5,17]. Thus, various business areassuch as communication, software systems, transportation, elec-tronics, education and research, manufacturing, services, IT andshipbuilding, aerospace, construction, packaging, textile industriesand supply chain management make use of the QFD methodology[18–20].
In the next subsection, a literature review on fuzzy set exten-sions in QFD is given.
2.2. Fuzzy set extensions in QFD
The QFD method is a useful analysis tool that is widely used inproduct design and development. To deal with challenges relatedto uncertainty and imprecision in QFD, various researchers havedeveloped many fuzzy QFD approaches by combining the fuzzyset theory with QFD. These approaches include conventional QFDcomputation methods using fuzzy variables [21,22], fuzzy out-ranking [23], entropy [24], incomplete fuzzy preference relations[25,26], multiple formatted fuzzy preference relations [27,28],fuzzy integral [29,30], fuzzy analytical network process [31,32],fuzzy multicriteria decision making (MCDM) [33,34], fuzzy goalprogramming [32,34], rough set based approach [35,36] and fuzzyexpert systems [37], among others. Interested readers can refer tofuzzy QFD literature survey articles (e.g. [38]) for more detailedinformation.
Reviewed literature suggests that these fuzzy QFD approachesusually concentrate on obtaining the importance ranking of CRsand/or DRs. However, relatively a small number of papers inves-tigate the selection process based on DRs. Our paper focuses on aDRs-based selection process.
Extended fuzzy set types include type-2 fuzzy sets, hesitantfuzzy sets, intuitionistic fuzzy sets, non-stationary fuzzy sets andfuzzy multisets. It is observed that the extended fuzzy sets arenew topics and rarely used as modeling tools in QFD. In one of thefirst studies, Li [39] applied 2-tuple linguistic representation modelunder multi-granularity linguistic environment in the construc-tion of HOQ. Ko [40] adopted a 2-tuple linguistic computationalapproach for constructing HOQ based failure modes and effectsanalysis, while Li et al. [41] handled software quality evaluationproblem based on the geometric aggregation operators with hes-itant fuzzy uncertain linguistic information. In another study, Liet al. [41] proposed an intuitionistic fuzzy set theory based QFD
approach for the knowledge management system selection prob-lem. In the proposed approach, the linguistic assessment data ofHOQ are transformed into intuitionistic fuzzy numbers and thealternatives are prioritized and ranked with the intuitionistic TOP-SIS method. Recently, Karsak and Dursun [42] employed a fusionof fuzzy information and 2-tuple linguistic representation model inthe QFD to calculate the weights of supplier selection criteria andsubsequently the ratings of suppliers.
3. Hesitant fuzzy linguistic term sets (HFLTS)
Hesitant fuzzy sets (HFSs) are the extensions of fuzzy sets whichcan solve the difficulties in determining the membership degree ofan element [7]. It represents the hesitancy where there are possible
values for membership and it is not clear which one is the rightvalue.
Definition 1. A hesitant fuzzy set (HFS) on X, where X is a fixedset, can be defined as follows:
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
E ={< x, hE (x) > |xεX
}(1)
where hE(x) denotes membership degrees of the element xεX to theset E and its values are in [0, 1].
S. C evik Onar et al. / Applied Soft Computing xxx (2016) xxx–xxx 3
HOQ i
[ff
tef[tHm
sat(hhooItttdap
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Fig. 1.
Hesitant fuzzy sets can be classified as dual hesitant fuzzy sets43], interval valued hesitant fuzzy sets [44], generalized hesitantuzzy sets [45], triangular fuzzy hesitant fuzzy sets [46] and hesitantuzzy linguistic term sets [6].
Experts may hesitate while selecting the appropriate linguis-ic expression. In the classical fuzzy linguistic approaches, a singlexpression should be selected which limits the experts. Hesitantuzzy linguistic terms sets (HFLTS) introduced by Rodriguez et al.6] can be used when the experts hesitate between several linguis-ic expressions. HFLTS itself, as well as the methods developed forFLTS enable representing and solving multiple linguistic assess-ents mathematically.
Chen and Hong [47] developed a new hesitant multicriteria deci-ion making approach that considers the pessimistic and optimisticttitudes of experts. Lee and Chen [48] proposed new aggrega-ion operators; namely, hesitant fuzzy linguistic weighted averageHFLWA), hesitant fuzzy linguistic weighted geometric (HFLWG),esitant fuzzy linguistic ordered weighted average (HFLOWA), andesitant fuzzy linguistic ordered weighted geometric (HFLOWG)perators for aggregating hesitant linguistic term sets and devel-ped a new fuzzy decision making method using these operators.
nstead of representing HFLTS with labels or intervals of linguis-ic terms, Wang et al. [49] used linguistic scale functions in theransformation process between qualitative information and quan-
Please cite this article in press as: S. C evik Onar, et al., A new hesitanselection, Appl. Soft Comput. J. (2016), http://dx.doi.org/10.1016/j.aso
itative data. Yavuz et al. [16] developed a HFLTS based multicriteriaecision making approach for alternative-fuel vehicle selectionnd applied their proposed model on a home health care servicerovider in the USA.
n QFD.
Basic definitions on HFLTS can be listed as follows [6,50]:
Definition 2. An HFLTS, Hs, is an ordered finite subset of consec-utive linguistic terms of a linguistic term set S which can be shownas S =
{s0, s1,. . ., sg
}.
Definition 3. Assume that EGH is a function that converts linguis-tic expressions into HFLTS, HS . Let GH be a context-free grammarthat uses the linguistic term set S. Let Sll be the expression domaingenerated by GH . This relation can be shown as EGH : Sll → HS .
Using the following transformations, comparative linguisticexpressions are converted into HFLTSs;
EGH (si) ={si|si ∈ S
}(2)
EGH (at mostsi) ={sj|sj ∈ Sand sj ≤ si
}(3)
EGH (lower thansi) ={sj|sj ∈ Sandsj < si
}(4)
EGH (at leastsi) ={sj|sj ∈ Sandsj ≥ si
}(5)
EGH (greater thansi) ={sj|sj ∈ Sandsj > si
}(6)
EGH(
betweensiandsj)
={sk|sk ∈ Sandsi ≤ sk ≤ sj
}(7)
Definition 4. The envelope of an HFLTS, represented by env (H ),
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
S
is a linguistic interval whose limits are obtained by its maximumand minimum values:
Table 1Linguistic scale for hesitant fuzzy AHP. Q12
Linguistic term si Abb. Triangular fuzzy number
Absolutely high importance s10 (AHI) (7,9,9)Very high importance s9 (VHI) (5,7,9)Essentially high importance s8 (ESHI) (3,5,7)Weakly high importance s7 (WHI) (1,3,5)Equally high importance s6 (EHI) (1,1,3)Exactly low importance s5 (EE) (1,1,1)Equally low importance s4 (ELI) (0.33,1,1)Weakly low importance s3 (WLI) (0.2,0.33,1)Essentially low importance s2 (ESLI) (0.14,0.2,0.33)
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ARTICLESOC 3560 1–16
S. C evik Onar et al. / Applied S
here
S− = min (si) = sj, si ∈ HSandsi ≥ sj∀i
S+ = max (si) = sj, si ∈ HSandsi ≤ sj∀i
efinition 5. Let S ={s0, s1, . . .sg
}be a linguistic term set. A
FLTS, HS , is defined as an ordered finite subset of consecutiveinguistic terms of S:
HS ={si, si+1, . . ., sj
}such that sk ∈ S, k ∈ {i, ..., j} (9)
efinition 6. An ordered weighted average (OWA) operator ofimension n is a mapping OWA: Rn → R, so that
WA (a1, a2, . . ., an) =∑n
j=1wjbj (10)
here bj is the jth largest of the aggregated arguments a1, a2, . . ., an,nd W = (w1, w2, . . ., wn)T is the associated weighting vector sat-sfying wi ∈ [0, 1] , i = 1, 2, . . ., n and
∑ni=1wi = 1.
efinition 7. A triangular fuzzy membership function A = (a, b, c)s used as the representation of the comparative linguistic expres-ions based on HFLTS HS , the definition domain of A should be theame as the linguistic terms
{si, ..., sj
}∈ HS . The min and the max
perators are used to compute a and c.
= min{aiL, aiM, ai+1
M , . . ., ajM, ajR
}= aiL (11)
= max{aiL, aiM, ai+1
M , . . ., ajM, ajR
}= aiR (12)
The remaining elements aiM, ai+1M , . . ., ajM ∈ T should contribute
o the computation of the parameter b. The aggregation operatorWA will be used to aggregate them:
= OWAWS
(aiM, ai+1
M , . . ., ajM
)(13)
. Hesitant fuzzy QFD: steps of the methodology
Hesitant Fuzzy Sets has the advantage of considering the hesi-ancy of experts under uncertainty. Neither classical QFD methodor ordinary fuzzy QFD method can handle this hesitancy.
In this section, we will first give the steps of the proposed hes-tant fuzzy QFD methodology and then extend the same steps forhe design problems having correlations among DRs.
.1. Steps of the proposed Hesitant Fuzzy QFD
Step 1. Identify and construct the hierarchy of customer require-ents as given in Fig. 2. Then determine the design requirements
orresponding to customer requirements.Step 2. Compute the weights of customer requirementsSteps 2.1–2.5 are applied to both the main customer require-
ents and the sub-customer requirements. The global weights ofub-customer requirements are calculated using steps 2.6–2.7.
Step 2.1: Construct pairwise comparison matrices for customerequirements and obtain the compromised evaluations from thexperts using HFLTS. The HFLTS are obtained by utilizing theinguistic terms in Table 1 and context-free grammar; such asetween, greater than, less than, at most, at least etc.
Step 2.2: Aggregate and build fuzzy envelope for HFLTS by using
Please cite this article in press as: S. C evik Onar, et al., A new hesitanselection, Appl. Soft Comput. J. (2016), http://dx.doi.org/10.1016/j.aso
he OWA operator, as proposed by Liu and Rodríguez [50]. In thispproach, the result of aggregation yields a trapezoidal fuzzy num-er. First, the scale given in Table 1 is sorted from the lowest (s0) tohe highest (sg). Assume the experts evaluations vary between two
terms i.e. si and sj . Then s0 ≤ si < sj ≤ sg . The parameters of trape-
zoidal fuzzy membership function A =(˛, ˇ, �, ı
)are computed
as follows:
= min{aiL, aiM, ai+1
M , . . ...ajM, ajR
}= aiL (14)
ı = max{aiL, aiM, ai+1
M , . . ...ajM, ajR
}= ajR (15)
=
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
aiM, if i + 1 = j
OWAw2
⎛⎝aiM, . . ...a
i + j
2M
⎞⎠ , if i + jiseven
OWAw2
⎛⎝aiM, . . ...a
i + j − 12
M
⎞⎠ , if i + jisodd
(16)
� =
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
ai+1M , if i + 1 = j
OWAw1
⎛⎝ajM, aj−1
M . . ...a
i + j
2M
⎞⎠ , if i + j is even
OWAw1
⎛⎝ajM, aj−1
M , . . ...a
i + j + 12
M
⎞⎠ , if i + j is odd
(17)
OWA operation given in Definition 6 requires a weight vector.Filev and Yager [51] define first and second types of weights usingthe � parameter which belongs to the unit interval [0,1]. First typeof weights W1 =
g−1 and g is the number of terms in theevaluation scale, j is the rank of highest evaluation and i is the rankof lowest evaluation value of the given interval.
S. C evik Onar et al. / Applied Soft Computing xxx (2016) xxx–xxx 5
Goal: Weigh�ng Customer
Requirements
Main Custom er Requirement 1
Sub-customer Requirement 11
...
Sub-customer
Main C ustom er Requirement 2
Sub-customer Requirement 21
...
Sub-customer
... Main C ustom er Requirement n
Sub-customer Requirement n1
...
Sub-custome r Requirement nv
customer requirements.
z[
c
m
r
m
w
mi
rr
r
w
w
(
w
w
uu
Table 2Linguistic scale for correlations.
Linguistic term Abb. Triangular fuzzy number
Absolutely low AL (1,2,3)Very low VL (2,3,4)Low L (3,4,5)Medium M (4,5,6)
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Requirement 1p Requirement 2t
Fig. 2. Hierarchy of
Since the fuzzy envelopes, obtained in previous step are trape-oidal fuzzy numbers, reciprocal values are calculated as follows8]:
˜ji = (1ciju,
1cijm2
,1cijm1
,1cijl
) (21)
Step 2.4: Compute fuzzy geometric mean for each row (ri) of theatrix C using Eq. (22).
i = (ci1 ⊗ ci2. . . ⊗ cin)1/n (22)
Step 2.5: The fuzzy weight (wCRi )of each main customer require-
ent is calculated using (ri) values as follows:
˜ CRi = ri ⊗ (r1 ⊕ r2. . . ⊕ rn)−1 (23)
In this study, the r1 ⊕ r2. . . ⊕ rn value is accepted as the maxi-um parameter of the linguistic term absolutely high importance
n Table 1 in order to decrease the deviation in the weights.This calculation process is same for the sub-customer
equirementswCRij , where j denotes the number of sub-customer
equirements belonging to the main customer requirement i.Step 2.6: Calculate the fuzzy global weights of sub-customer
equirements by using Eq. 24.
˜ Gij = wCR
i × wCRij (24)
here wGij is the global weight of sub-customer requirement ij.
Step 2.7: Defuzzify the trepozoidal fuzzy numbers wGij using Eq.
25) and normalize the defuzzified values using Eq. (26).
Gij = ˛ + 2 + 2� + ı
6(25)
Nij =
wGij∑
i
∑jw
Gij
(26)
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Step 3. Collect the data for the relations between DRs and CRs bysing HFLTS from experts. The HFLTS of relations are obtained bytilizing the linguistic terms in Table 2 and context-free grammar.
High H (5,6,7)Very high VH (6,7,8)Absolutely high AH (7,8,9)
Step 4. Aggregate HFLTS relations by using the aggregationoperator defined in Step 2.2 and obtain relation matrix R withtrapezoidal fuzzy numbers as given by Eq. (27).
R =
DR1 DR2 · · · DRz
CR11
CR12
...
CRnv
⎡⎢⎢⎢⎢⎣R111 R112 · · · R11z
R121 R122 · · · R12z
......
. . ....
Rnv1 Rnv2 · · · Rnvz
⎤⎥⎥⎥⎥⎦
(27)
Step 5. Obtain weighted relation matrix (Rw)whose elements areobtained by using Eq. (28)
Rwijk = wNij × Rijk (28)
Step 6. Obtain fuzzy importance values of DRs by summing theelements in each column of Rw as shown in Eq. (29).
DRImpk =
∑i
∑j
Rwijk (29)
where DRImpk denotes the fuzzy importance of design require-
ment k.Step 7. Using Eqs. (25) and (30), obtain the crisp importance
weights of DRs by defuzzifying DRImpk and normalizing them.
DRNk = DRImpk
maxk=1,....z
DRImpk
(30)
where DRImpk
and DRNk denote the defuzzified and normalized
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
importance values of design requirement k, respectively.Step 8. Collect the HFLTS from experts to evaluate alternatives
with respect to DRs by utilizing the linguistic terms listed in Table 2and context-free grammar.
Step 9. Apply the hesitant fuzzy TOPSIS method to prioritize thelternatives.
Step 9.1. Aggregate HFLTS evaluations by using the aggrega-ion operator defined in Step 2.2 in order to obtain decision matrixomposed of trapezoidal fuzzy numbers.
˜ =
DR1 DR2 · · · DRz
A1
A2
...
AL
⎡⎢⎢⎢⎢⎣�11 �12 · · · �1z
�21 �22 · · · �2z
......
. . ....
�L1 �L2 · · · �Lz
⎤⎥⎥⎥⎥⎦
(31)
here �ij =(�ijl , �ijm1
, �ijm2, �iju
).
Step 9.2: Build a normalized decision matrix DN by using Eq.33).
˜N =
DR1 DR2 · · · DRz
A1
A2
...
AL
[
�N1z �N12 · · · �N1z
�N21 �N22 · · · �N2z
......
. . ....
�NL1 �NL2 · · · �NLz
](32)
˜Nij = �ijmaxi=1,...,L
�ij, j = 1, . . ., z (33)
Step 9.3: Obtain the weighted normalized decision matrix DNwy using Eq. (35).
Step 9.3: Obtain the weighted normalized decision matrix DNwy using Eq. (35).
Step 9.4: Calculate the distances of each alternative fromositive A
+ =(v+
1 , . . ., v+p
)and negative A
− =(v−
1 , . . ., v−p
)ideal
olutions by defining v+i = (1, 1, 1, 1) and v−
i = (0, 0, 0, 0).
+i =
z∑j=1
d(�Nwij, v+i ) (36)
here
(�Nwij, v+i ) =
√14
[(1 − �Nwijl
)2 + (1 − �N
wijm1)2 + (1 − �N
wijm2)2 + (1 −
and
−i =
∑Z
j=1d(�Nwij, v
−i ) (38)
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here
(�Nwij, v−i ) =
√14
[(0 − �Nwijl
)2 + (0 − �N
wijm1)2 + (0 − �N
wijm2)2 + (0 − �N
wij
Fig. 3. Correlations among DRs.
Step 9.5: Calculate the closeness coefficient of each alternativeand rank the alternatives.
CCi = d−i
d+i + d−
i
(40)
In the next subsection, we will consider the correlations amongdesign requirements in order to reflect the inner dependencies ofDRs on the weighted relation matrix.
4.3. Consideration of correlations among design requirements
In this section we assume that there exist correlations amongDRs. In this case, the compromised correlations among DRs, cij , areexpressed by experts using HFLTS based on the linguistic scale thatwas provided in Table 2. In Fig. 3, the roof of HOQ shows thesecorrelations.
These correlations among DRs are aggregated by using theaggregation operator defined in Step 2.2 to obtain the relationmatrix C with trapezoidal fuzzy numbers.
C =
DR1 DR2 · · · DRz
DR1
DR2
...
DRz
⎡⎢⎢⎢⎢⎣cc11 cc12 · · · cc1z
cc22 · · · cc2z
. . ....
cczz
⎤⎥⎥⎥⎥⎦
(41)
Normalized relation matrix Rnorm
is formed as follows:
Rnorm =
DR1 DR2 · · · DRz
CR11
CR12
⎡⎢⎢⎢R
norm111 Rnorm
112 · · · Rnorm11z
Rnorm121 Rnorm
122 · · · Rnorm12z
⎤⎥⎥⎥ (42)
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
Table 4Pairwise comparisons of the main CRs with respect to the goal.
Performance Mobility Peripherals
Performance EE Between EHI and WHI Between ELI and EHI
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
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477
478
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481
482
483
484
485
486
487
488
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490
491
492
ARTICLESOC 3560 1–16
S. C evik Onar et al. / Applied S
here
˜normij,k =
∑zl=1
(Rij,l ⊗ ccl,k
)∑zk=1
∑zl=1
(Rij,k ⊗ cck,l
) , ij = 11, 12, . . ., nv (43)
In this case, the weighted relation matrix (Rw)is obtained bysing Eq. (44).
˜wijk = wNij × Rnorm
ij,k (44)
The rest of the methodology is composed of the same steps givenn Section 4.1.
. Case study
In this section, three computer workstations are compared bysing the proposed hesitant QFD method based on the determinedRs and DRs. First we give the problem definition and implementhe proposed method to the computer workstation selection prob-em. Later, a sensitivity analysis and comparisons with classical andrdinary fuzzy QFD approaches are presented.
.1. Problem definition
Based on the QFD method, this paper aims to carry out the selec-ion of the most suitable computer workstation that fulfills designequirements determined according to customer expectations. Aorkstation is a customized computer that is designed for spe-
ific scientific or technical application. Such equipment is usuallyntegrated within a local network and has a multi-user operatingystem that is able to be run be a single person. In the past, everyomputer connected to the internet was used to be called a work-tation. However, this definition of a workstation is a thing of theast, thanks to the technological advancements (mostly due to 3Dnimations) by certain companies such as Sun Microsystems, Sili-on Graphics, Apollo Computer, HP and IBM. Compared to personalomputers, workstations are able to provide a higher performanceo end users. This improved performance is usually based on the usef higher-end computer components like microprocessor (CPU),raphics processing unit (GPU), physical memory and other partshat ensure multitasking.
.2. Identification of customer requirements and expectations
The target customer group of workstations includes computer-ided designers, digital content creators, financial servicesmployees, software developers, power office employees, analystsnd printmakers.
Computer-aided designers: Professionals in this group are largelyccupied with 2D and 3D modeling with the help of computeroftware. It also includes industrial and mechanical engineers whoesign specific components, as well as architects and civil engineersho design buildings. This group basically expects high resolution
creens and capable graphics cards.Digital content creator: Various fields can be categorized within
his group, such as GPS maps, meteorological maps and multime-ia (videos, sound and pictures). Professionals working as digitalontent creators need multitasking capabilities, a powerful CPU asell as high performing GPUs.
Financial services employees: This profession usually works withnancial calculation algorithms that need to be computed fastnough to obtain the results in a short time. This translates into
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arge amounts of physical memory to store data and workhorseicroprocessors.
Software Developers: Developers usually tend to work on the go,nd prefer mobility over other needs. Therefore their expectations
Mobility EE Between WLI and ELIPeripherals EE
are more focused on long battery life, rather than processing poweror other specifications.
Power Office employees: People who usually work with Officeapplications can be categorized within this group. This user profilebasically needs a fair level of processor performance and robustcomputer case.
Analysts: This profession group mainly requires computers withhigh processing power.
Printmakers: Graphical designers work in front of big screensand need large amounts of GPU power. In addition, software theyuse usually requires high-capacity physical memory components.
The proposed approach is applied for the workstation selectionproblem of a large IT company, which includes the entire customergroups mentioned above. A group of three experts has supportedthe process. The expert group has identified 14CRs in three maindimensions, as shown in Table 3. This corresponds to Step 1 in ourproposed approach.
In the computer market, there are several workstation manufac-turers. In this study, we considered the following three workstationmanufacturers based on the experts opinions:
Company G is a Taiwan-based company established in 1986. Thecompany manufactures motherboards, motherboard components,notebooks, desktop PCs, servers and mobile phones. Company G isone of the top 20 companies in Taiwan and its market capitalizationis 133 million USD.
Company H is a large international conglomerate which is basedin Palo Alto, California, USA. It manufactures hardware for data pro-cessing, printing solutions and digital image products. It is also asoftware and service provider. In 2002, Company H merged withanother international computer company. Its operating systemsand microprocessors are well known in the market. Company Halso produces servers and workstations and management software.
Company A is one of the leading mobile phone and computerproducers. Company A’s computers are well known for their capa-bilities in graphical design related tasks. It started to use Intelchips in all its products. In 2009, Company A announced that theystarted building their own engineering team to design customizedmicrochips.
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
Fig. 4 illustrates the HFLTS assessments between DRs and CRs inthe House of Quality (HOQ). We give here only a small part of thehuge HOQ matrix because of space constraints. The whole detailscan be found in Tables 4–7 and 10.
8 S. C evik Onar et al. / Applied Soft Computing xxx (2016) xxx–xxx
Table 5Pairwise comparisons of the sub-customer requirements with respect to performance.
Data processing (CR11) Image processing (CR12) Image production (CR13) Program production (CR14) Gaming (CR15)
Data processing (CR11) EE Between ELI and EHI Between ESLI and ELI Between EHI and WHI Between EHI and ESHIImage processing (CR12) EE Between ELI and EHI Between WLI and EE ELIImage production (CR13) EE Between ELI and EHI Between EHI and WHIProgram production (CR14) EE Between EHI and WHIGaming (CR15) EE
Table 6Pairwise comparisons of the sub-customer requirements with respect to mobility.
Charging time (CR21) Battery life (CR22) Weight (CR23) Thickness (CR24)
Charging time (CR21) EE Between ALI and ESLI Between ESLI and ELI Between ELI and EHIBattery life (CR22) EE Between EHI and WHI Between EHI and WHIWeight (CR23) EE Between EHI and ESHIThickness (CR24) EE
Table 7Pairwise comparisons of the sub-customer requirements with respect to peripherals.
Display connectivity (CR31) EE Between ELI and EHI Between ESLI and ELI Between EHI and WHI Between EHI and ESHIUniversal connectivity (CR32) EE Between WLI and ELI Between ELI and EHI Between ELI and EHIAdapter (CR33)
Sound (CR34)
Display (CR35)
Wei
ghts
CPU
GPU …
Build
qua
lity
CR11 (0.01 ,0.04,0.16 ,1.45)
Betwee n H and AH
... .. .
CR12 (0,0.04,0.13,0.89 )Betwee n L
and MBetwee n VH
and AH ... .. .
... .. . ... .. . .. . .. .
CR35 (0,0.02,0.07,0.72 ) …Betwee n M
and H
CPU
GPU …
Build
qua
lity
AH Betwee n M and H
... Betwee n H and AH
Between VH and AH
Between L and M
... Between H and AH
Betwee n M and H
Betwee n VL and L ...
Betwee n M and H
s e vita nret lA
Compa ny A
Company H
Compa ny G
w
5
TCe
as follows:
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516517
518
519
520
521
522
523
524
525
526527
528
529
530531
Fig. 4. Assessment using HFLTS in HOQ.
In the next subsection, we implement the proposed method toorkstation selection problem.
.3. Implementation
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To compute the weights of CRs (Step 2) we use the followingables 4–8. Table 4 shows the pairwise comparisons of the mainRs with respect to the goal, filled by the experts’ compromisedvaluation using HFTLS. Tables 5–7 present the pairwise compar-
EE Between WLI and EE Between EHI and ESHIEE Between WHI and ESHI
EE
isons of the sub-customer requirements with respect to the mainCRs Performance, Mobility and Peripherals, respectively.
Applying Steps 2.1–2.5 we obtain Table 8. In order to facili-tate the understandability of the approach we give an example ofcalculations in the following:
Table 8 shows that the pairwise comparison value of Perfor-mance and Mobility is calculated as (1, 1, 3, 5). The linguisticevaluations of the experts for this comparison are between“s6 = Equally High Importance” and “s7 = Weakly High Importance”.The triangular fuzzy numbers associated with the mentioned lin-guistic terms are (1, 1, 3) and (1, 3, 5), respectively. Using theformulas given in Eqs. (14)–(17), the trapezoidal fuzzy member-ship function A =
(˛, ˇ, �, ı
)representing the linguistic evaluation
is calculated as:
= min{a6L, a7
L, a6M, a7
M, a6R, a7
R
}= min
{1, 1, 1, 3, 3, 5
}= 1
ı = max{a6L, a7
L, a6M, a7
M, a6R, a7
R
}= max
{1, 1, 1, 3, 3, 5
}= 5
and since i + 1 = j (i = 6, j = 7);
= a6M = 1
� = a7M = 3
After determining the pairwise comparison values for eachexpert evaluation, the normalized weight of each criterion is cal-culated next. To this end, the geometric mean of each row iscalculated. For example, the (0.69, 1, 1.44, 2.47) value in Table 8is calculated as:
Next, the geometric mean of each row is divided by the sumf geometric means using Eq. (30). The normalized weight for theriterion Performance is obtained as follows:
0.695.93
= 0.12;1
3.88= 0.26;
1.442.48
= 0.58;2.471.72
= 1.43
Steps 2.1–2.5 are repeated to obtain the relative scores in Table 9.teps 2.6 and 2.7 are applied to calculate the normalized weights ofhe sub-customer requirements as given in Table 9. As an examplealculation, the fuzzy global weight of data processing (CR11) isalculated by using Eq. (24) as follows:
hen we defuzzify the trepozoidal fuzzy numbers wG11 using Eq.
25), we obtained the following result.
G11 = 0.006 + 2 × 0.042 + 2 × 0.165 + 1.447
6= 0.311
To calculate the normalized value 0.093, we first sum theefuzzified values and then the defuzzified value 0.311 is dividedy this sum.
N11 = 0.311
3.327= 0.093
Table 10 presents the relations between design requirementsnd customer requirements by using the compromised HFLTSbtained from the three experts. Table 11 presents the aggregatedelation matrix R between CRs and DRs.
Using Eqs. (14)–(19) and Table 2, the aggregated value for CR11nd CPU relation which corresponds to “Between H and AH” is cal-ulated as (5,6.83,7.17,9).
Table 12 shows the weighted relation matrix (Rw) and the fuzzymportance values of DRs. The weighted correlation for CR11 andPU relation is calculated as follows:
.093 × 5, 6.83, 7.17, 9 = 0.47, 0.64, 0.67, 0.84
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( ) ( )
The crisp importance weights of DRs are given in Table 13.he defuzzified score for CPU is calculated as follows: First, theeighted correlations in the CPU column in Table 12 are summed.
It is found to be DRImpCPU = (1.74, 2.36, 2.58, 3.2). Then this sum is
defuzzified using Eq. (25) to calculate DRNCPU:
DRNCPU = 1.74 + 2 × 2.36 + 2 × 2.58 + 3.26
= 2.47
The normalized score is calculated by using Eq. (30).
DRNCPU = 2.472.805
= 0.881
Thus, the process for weighting the DRs has been completed. Thenext step is to apply fuzzy TOPSIS. Table 14 presents the decisionmatrix including the HFLTS evaluations of the experts.
The evaluation of the alternatives with respect to the DRs isgiven in Table 15. According to these results, the best workstationalternative is Company H. Even their scores are very close to eachother, the second and third alternatives are ranked as Company Aand Company G, respectively.
Applying Steps 9.1–9.5 Table 15 is obtained. It presents the eval-uation of alternatives with respect to DRs.
When we analyze the values in Table 15, we see that CompanyA is performing extremely poor in VGA and HDMI, while CompanyG is scoring extremely poor in CPU, GPU and charging power. Com-pany H is the worst in memory but only moderately, which causesit to be the best.
In the next subsection, a sensitivity analysis is given in order toexamine the robustness of the given decision.
5.4. Sensitivity analysis
To observe the effects of the possible changes in the weightsof the DRs on the computer workstation selection, a sensitivityanalysis is conducted. In Fig. 5, one-at-a time sensitivity analysishas been applied. In this figure, the colors blue, orange and greyrepresent the alternatives A, H and G, respectively. The x-axis rep-resents the criterion weight, while the y-axis represents the scoresof alternatives.
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
In the sensitivity analysis, we change the value of a certain cri-terion’s weight as the other criteria weights are fixed. Using thesenew criteria weights, the scores of alternatives are recalculated.The dark red line represents the current weight of the DR. Selec-
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ARTICLE IN PRESSG ModelASOC 3560 1–16
S. C evik Onar et al. / Applied Soft Computing xxx (2016) xxx–xxx 11
Table 11Aggregated relation matrix R between CRs and DRs.
Weight CPU GPU Memory Operating system Charging power Battery Cells VGA
12 S. C evik Onar et al. / Applied Soft Computing xxx (2016) xxx–xxx
Table 13Weights of design requirements.
DRs Defuzzified score Normalized score
CPU 2.47 0.881GPU 1.678 0.598Memory 2.3 0.82Operating System 0.9817 0.35Charging power 1.2367 0.441Battery Cells 1.6317 0.582VGA 1.1283 0.402HDMI 0.8517 0.304Speakers 0.8167 0.291Cooling Fan 2.805 1USB 0.4317 0.154Display 1.545 0.551Build quality 0.625 0.223
Table 14Evaluation of alternatives with respect to design requirements.
CPU GPU Memory Operating System Charging power Battery Cells VGA
Company A AH Between M and H M AH Between VH and AH Between L and H ALCompany H Between VH and AH Between L and M Between L and M H Between VH and AH Between L and H AHCompany G Between M and H Between VL and L Between M and H Between VH and AH Between AL and VL Between H and AH AH
HDMI Speakers Cooling fan USB Display Build quality
Company A AL M Between M and VH Between H and VH Between H and AH Between H and AHCompany H AH M Between M and H Between H and AH Between H and VH Between H and AHCompany G AH Between M and H Between VH and AH M M Between M and H
Table 15Evaluation of alternatives with respect to DRs.
ion of alternative H is a robust decision and the changes in theeights of the DRs do not affect the selection of H whereas small
hanges in the weights of DRs affect the ranking of alternatives And G. When the weights of the DRs HDMI, battery cells, VGA andpeakers become larger than their present values, then the alter-ative G takes the second rank. Similarly, a slight decrease in theeights of DRs CPU, GPU, charging power and display causes alter-
ative A to take the third order. The most insensitive DRs are USB,emory, Cooling Fan, and Build Quality since the functions of the
lternatives do not have almost any intersection along the axis ofhe related DR weight.
In the next subsection, we compare our proposed method withoth classical QFD and ordinary fuzzy QFD.
.5. Comparison with the classical QFD and ordinary fuzzy QFD
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pproaches
In this section, we used the classical QFD and ordinary fuzzy QFDpproaches for evaluating computer work stations.
8.335 8.5334.829 4.6520.367 0.353
For the comparison with classical QFD, the same experts areasked to make a compromise evaluation by using crisp values.The results of our proposed method have been compared with theresults of the classical QFD method. Table 16 presents the DRs’ crispweights, the evaluation of each alternative with respect to each DRand the total score of alternatives.
According to the overall result of classical QFD, Alternative H isthe best alternative followed by G and A. The selection of the Alter-native H remains the same as the result of our proposed method,however the rankings of alternatives G and A are different.
For the comparison with ordinary fuzzy QFD, the same expertsare asked to make a linguistic evaluation using scale in Table 2. Inorder to apply ordinary fuzzy QFD, simple fuzzy additive weight-ing method is used. Table 17 presents these linguistic evaluationsand the scores of alternatives obtained through ordinary fuzzy QFDapproach.
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
According to the overall result of ordinary fuzzy QFD, AlternativeH is the best alternative followed by A. The obtained rank is thesame as the rank in classical QFD approach.
Table 18 shows the ranking of the companies with respect to
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FD approaches.The experts indicate that the results obtained with the hesitant
uzzy QFD method are more meaningful when compared to thelassical and ordinary fuzzy QFD approaches. The differences in the
Fig. 5. Sensitivity analysis. (For interpretation of the references to colour
PRESSmputing xxx (2016) xxx–xxx 13
scores of alternatives come from the hesitant evaluations in the
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
proposed method. In ordinary fuzzy QFD, experts have to selectone of the linguistic terms falling into the interval evaluations inTable 14, which forces experts to make a discrete selection whereashesitant fuzzy QFD enables aggregated linguistic term sets based on
in the text, the reader is referred to the web version of this article.)
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ARTICLE IN PRESSG ModelASOC 3560 1–16
14 S. C evik Onar et al. / Applied Soft Computing xxx (2016) xxx–xxx
Table 18Ranking of the companies with respect to QFD approaches.
Company A Company H Company G
Om
6
EbofpQtc
pmccetcdnes
iohtoThT
Q8
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
Hesitant Fuzzy QFD 2
Classical QFD 3
Ordinary Fuzzy QFD 3
WA operator to be used. Therefore, hesitant evaluations provideore flexible and informative representation of uncertainty.
. Conclusion
Hesitancy is an inherent part of decision making process.xperts generally have difficulty to establish the degree of mem-ership of fuzzy set because of the time pressure, lack of knowledger data, etc. To overcome these difficulties, the concept of hesitantuzzy set which permitted the membership degree having a set ofossible values can be employed. We have proposed hesitant fuzzyFD since it can reflect the human’s hesitancy more objectively
han the other classical extensions of fuzzy set and applied it toomputer workstation selection problem.
A computer workstation is a fast and capable individual com-uter for professional use. Usually, companies that need fastericroprocessors, larger RAMs and higher speed prefer using
omputer workstations. Computer workstation selection is a multi-riteria problem under fuzzy environment since experts generallyxpress their evaluations by using linguistic terms. In this paper,his selection process has been supported with a QFD approach,onsidering the DRs associated with the CRs. The best alternative isetermined by weighting the DR scores and calculating the close-ess coefficient for each alternative. A model that considers theffects of correlations among DRs in the computer workstationelection process has also been proposed.
These proposed methods enabled us to analyze the vague andmprecise relations between CRs and DRs. The determined weightsf CRs, which are obtained with the hesitant fuzzy AHP technique,ave been reflected to the workstation selection by using a hesi-ant fuzzy TOPSIS method. Thus, a flexible evaluation process based
Please cite this article in press as: S. C evik Onar, et al., A new hesitanselection, Appl. Soft Comput. J. (2016), http://dx.doi.org/10.1016/j.aso
n HFLTS, which reflects experts’ hesitancies, has been designed.he main contribution of this study is the consideration of experts’esitancies in each phase of the QFD approach for the first time.he Adapter and image production specifications have been deter-
[
1 31 21 2
mined as the most important CRs whereas cooling fan and CPU havebeen determined as the most important DRs.
The conducted sensitivity analysis indicated that the best alter-native (H) is not sensitive to the changes in the weights of DRswhereas the rankings of other alternatives (A and G) are sensitiveto even the slightest changes in the weights of DRs. Our compara-tive analysis produced a different ranking result due to the abilityof the hesitant fuzzy method in handling the uncertainty better.
For further research, instead of the OWA operator, other aggre-gation operators such as hesitant interval-valued fuzzy weightedaveraging operator or hesitant interval-valued fuzzy orderedweighted averaging operator can be used. We also suggest intu-itionistic fuzzy sets to be used in QFD instead of hesitant fuzzy setssince intuitionistic fuzzy sets can consider both membership andnon-membership functions in their definitions.
References
[1] L.P. Sullivan, Quality function deployment: a system to assure that customerneeds drive the product design and production process, Qual. Prog. (June)(1986) 39–50.
[2] Y. Akao, Quality Function Deployment: Integrating Customer RequirementsInto Product Design, Taylor & Francis, 1990.
[3] J.R. Hauser, D. Clausing, The house of quality, Harvard Business Review
(May–June) (1988) 63–73.[4] M.L. Shillito, Advanced QFD—Linking Technology to Market and Company
Needs, Wiley, New York, 1994.[5] B. Prasad, Reviewof QFD and related deployment techniques, J. Manuf. Syst.
(1998) 221–234.[6] R.M. Rodriguez, L. Martinez, F. Herrera, Hesitant fuzzy linguistic term sets for
decision making, IEEE Trans. Fuzzy Syst. 20 (2012) 109–118.[7] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010) 529–539.[8] S. C evik Onar, B. Öztays i, C. Kahraman, Strategic decision selection using
hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP: a case study, Int. J.Comput. Intell. Syst. 7 (2014) 1002–1021.
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
[9] H. Liao, Z. Xu, X.J. Zeng, J.M. Merigó, Qualitative decision making withcorrelation coefficients of hesitant fuzzy linguistic term sets, Knowl. BasedSyst. 76 (2015) 127–138.
10] H. Liao, Z. Xu, Approaches to manage hesitant fuzzy linguistic informationbased on the cosine distance and similarity measures for HFLTSs and their
application in qualitative decision making, Expert Syst. Appl. 42 (2015)5328–5336.
11] J.Q. Wang, J. Wang, Q.H. Chen, H.Y. Zhang, X.H. Chen, An outranking approachfor multi-criteria decision-making with hesitant fuzzy linguistic term sets, Inf.Sci. 280 (2014) 338–351.
12] B. Zhu, Z. Xu, Consistency measures for hesitant fuzzy linguistic preferencerelations, IEEE Trans. Fuzzy Syst. 22 (2014) 35–45.
13] N. Zhang, Hesitant fuzzy linguistic information aggregation in decisionmaking, Int. J. Oper. Res. 21 (2014) 489–507.
14] Z. Zhang, C. Wu, Hesitant fuzzy linguistic aggregation operators and theirapplications to multiple attribute group decision making, J. Intell. Fuzzy Syst.26 (2014) 2185–2202.
15] R.M. Rodríguez, H. Liu, L.A. Martínez, Fuzzy representation for the semanticsof hesitant fuzzy linguistic term sets, Adv. Intell. Syst. Comput. 277 (2014)745–757.
16] M. Yavuz, B. Oztaysi, S. Cevik Onar, C. Kahraman, Multi-criteria evaluation ofalternative-fuel vehicles via a hierarchical hesitant fuzzy linguistic model,Expert Syst. Appl. 42 (2015) 2835–2848.
17] Y.H. Tseng, C.T. Lin, Enhancing enterprise agility by deploying agile drivers,capabilities and providers, Inf. Sci. 181 (2011) 3693–3708.
18] L.K. Chan, M.L. Wu, Quality function deployment: a literature review, Eur. J.Oper. Res. (2002) 463–497.
19] Y. Akao, G.H. Mazur, The leading edge in QFD: Past, present and future, Int. J.Qual. Reliab. Manag. 20 (2003) 20–35.
20] J.A. Carnevalli, P.C. Miguel, Review, analysis and classification of the literatureon QFD-Types of research, difficulties and benefits, Int. J. Prod. Econ. 114(2008) 737–754.
21] L.P. Khoo, N.C. Ho, Framework of a fuzzy quality function deployment system,Int. J. Prod. Res. 34 (1996) 299–311.
22] X.X. Shen, K.C. Tan, M. Xie, The implementation of quality functiondeployment based on linguistic data, J. Intell. Manuf. 12 (2001) 65–75.
23] J. Wang, Fuzzy outranking approach to prioritize design requirements inquality function deployment, Int. J. Prod. Res. 37 (1999) 899–916.
24] L.K. Chan, H.P. Kao, A. Ng, M.L. Wu, Rating the importance of customer needsin quality function deployment by fuzzy and entropy methods, Int. J. Prod.Res. 37 (1999) 2499–2518.
25] G. Büyüközkan, G. C ifc i, A new incomplete preference relations basedapproach to quality function deployment, Inf. Sci. 206 (2012) 30–41.
26] G. Büyüközkan, G. C ifc i, An integrated QFD framework with multipleformatted and incomplete preferences: a sustainable supply chainapplication, Appl. Soft Comput. 13 (2013) 3931–3941.
27] G. Büyüközkan, O. Feyzioglu, Group decision making to better respondcustomer needs in software development, Comput. Ind. 48 (2005) 2005.
28] G. Büyüközkan, O. Feyzioglu, D. Ruan, Fuzzy group decision making tomultiple preference formats in quality function deployment, Comput. Ind. 58(2007) 392–402.
29] C.Y. Tsai, Using fuzzy QFD to enhance manufacturing strategic planning, J.Chin. Inst. Ind. Eng. 18 (2003) 33–41.
30] O. Feyzioglu, G. Büyüközkan, An integrated group decision-making approach
Please cite this article in press as: S. C evik Onar, et al., A new hesitanselection, Appl. Soft Comput. J. (2016), http://dx.doi.org/10.1016/j.aso
for new product development, Int. J. Comput. Integr. Manuf. 21 (2008)366–375.
31] T. Ertay, G. Büyüközkan, C. Kahraman, D. Ruan, Quality function deploymentimplementation based on analytic network process with linguistic data: anapplication in automotive industry, J. Fuzzy Intell. Syst. 16 (2005) 221–232.
[
[
817
PRESSmputing xxx (2016) xxx–xxx
32] C. Kahraman, T. Ertay, G. Büyüközkan, A fuzzy optimization model for QFDplanning process using analytic network approach, Eur. J. Oper. Res. 171(2006) 390–411.
33] M. Celik, S. Cebi, C. Kahraman, I.D. Er, An integrated fuzzy QFD model proposalon routing of shipping investment decisions in crude oil tanker market,Expert Syst. Appl. 36 (2009) 6227–6235.
34] Z. Ayag, F. Samanlioglu, G. Büyüközkan, A fuzzy QFD approach to determinesupply chain management strategies in the dairy industry, J. Intell. Manuf. 24(2013) 1111–1122.
35] Y.L. Li, J.F. Tang, K.S. Chin, Y. Han, X.G. Luo, A rough set approach forestimating correlation measures in quality function deployment, Inf. Sci. 189(2012) 126–142.
37] C.K. Kwong, Y. Chen, H. Bai, D.S.K. Chan, A methodology of determiningaggregated importance of engineering characteristics in QFD, Comput. Ind.Eng. 53 (2007) 667–679.
38] M. Abdolshah, M. Morad, Fuzzy quality function deployment: an analyticalliterature review, J. Ind. Eng. (2013), Article ID 682532 11.
39] M. Li, The extension of quality function deployment based on 2-tuplelinguistic representation model for product design under multigranularitylinguistic environment, Math. Probl. Eng. (2012), Article ID 989284 18.
40] W.-C. Ko, Exploiting 2-tuple linguistic representational model forconstructing HOQ-based failure modes and effects analysis, Comput. Ind. Eng.64 (2013) 858–865.
41] Q. Li, X. Zhao, G. Wei, Model for software quality evaluation with hesitantfuzzy uncertain linguistic information, J. Intell. Fuzzy Syst. 26 (2014)2639–2647.
42] E.E. Karsak, M. Dursun, An integrated fuzzy MCDM approach for supplierevaluation and selection, Comput. Ind. Eng. 82 (2015) 82–93.
43] S. Pushpinder, A new method for solving dual hesitant fuzzy assignmentproblems with restrictions based on similarity measure, Appl. Soft Comput.24 (2014) 559–571.
44] P. Quiros, P. Alonso, H. Bustince, I. Díaz, S. Montes, An entropy measuredefinition for finite interval-valued hesitant fuzzy sets, Knowl. Based Syst. 84(2015) 121–133.
45] G. Qian, H. Wang, X. Feng, Generalized hesitant fuzzy sets and theirapplication in decision support system, Knowl. Based Syst. 37 (2013) 357–365.
46] D. Yu, Triangular hesitant fuzzy set and its application to teaching qualityevaluation, J. Inf. Comput. Sci. 10 (2013) 1925–1934.
47] S.-M. Chen, J.-A. Hong, Multicriteria linguistic decision making based onhesitant fuzzy linguistic term sets and the aggregation of fuzzy sets, Inf. Sci.286 (2014) 63–74.
48] L.W. Lee, S.-M. Chen, Fuzzy decision making based on likelihood-basedcomparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzylinguistic operators, Inf. Sci. 294 (2015) 513–529.
based on hesitant fuzzy linguistic term sets: an outranking approach, Knowl.Based Syst. 86 (2015) 224–236 (in press).
t fuzzy QFD approach: An application to computer workstationc.2016.04.023
50] H. Liu, R.M. Rodríguez, A fuzzy envelope for hesitant fuzzy linguistic term setand its application to multicriteria decision making, Inf. Sci. 258 (2014)220–238.
51] D. Filev, R.R. Yager, On the issue of obtaining OWA operator weights, FuzzySets Syst. 94 (1998) 157–169.
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