Research Article An Experimental Research Study on the ...

Research ArticleAn Experimental Research Study on the Solution of a PrivateSmall Hydropower Plant Investments Selection Problem byELECTRE IIIIV Shannonrsquos Entropy and Saatyrsquos SubjectiveCriteria Weighting

Burak Omer Saracoglu12

1 Institute of Science amp Technology Istanbul Technical University 34469 Istanbul Turkey2Faculty of Naval Architecture amp Ocean Engineering Istanbul Technical University 34469 Istanbul Turkey

Correspondence should be addressed to Burak Omer Saracoglu burakomersaracogluhotmailcom

Received 23 August 2014 Revised 18 November 2014 Accepted 20 December 2014

Academic Editor Roger Z Rıos-Mercado

Copyright copy 2015 Burak Omer Saracoglu This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Almost all of the todayrsquos modern daily life conditions of humankind depend on the electricity The countries either by onlythemselves or sometimes with some international intuitions andor organizations have been trying to find the best methods waysand projects to supply the electricity to their societies One of the important tools for the countries to increase the amount andquality of the electricity generation is to activateigniteinitiate the private investment capabilitiesopportunities The electricitygeneration market in Turkey is a freeopen market for both the foreign and domestic private investors Hence both the foreignand domestic private investors have been looking for the most suitable electricity generation plant projects Small hydropowerplant (SHPP) investments (SHPPIs) are one of the alternatives in the Turkish electricity generationmarket especially for the privateinvestors searching for the renewable energy investments This experimental research study investigates the possibility of using theELECTRE IIIIV Shannonrsquos Entropy and Saatyrsquos Analytic Hierarchy Process (AHP) subjective weighting (for criteria) methods forthe solution of this problem In the experimental case study the most appropriate SHPPIs amongst five alternative SHPPIs at theSHPPIsrsquo predevelopment investment stages in Turkey were evaluated and ranked in order

1 Introduction

The peak load and the electricity consumption in Turkeyhave been increasing in almost steady conditions since 1996as presented in Table 1 The causes of this almost steadyelectricity demand increase condition are mainly given as theincrease in the population in Turkey and the increase in theincome growth in Turkey by the researchers (see and readsome studies on this issue [1ndash3])

These increasing conditions of the population and thegross domestic product (GDP) in Turkey are presented by thehelp of the historical data as shown in Figure 1 for expressingand showing the actual situation of these conditions veryclearly and plainly to the researchers the academics theprivate investors and the whole readers

In addition to these historical data several projectionstudies for these two indicators present that the growth statuswill continue in the long term (see and read some studies onthis issue [1ndash3])

The location of Turkey is very interesting and strategic inthe point of view of the geographical geopolitical and socioe-conomic research studies (see and read [4ndash6]) Turkey is atranscontinental (Europe and Asia) country that has the landboundaries with Syria (822 km) (southeast) Iran (499 km)(east) Iraq (352 km) (southeast) Armenia (268 km) (east)Georgia (252 km) (northeast) Bulgaria (240 km) (north-west) Greece (206 km) (west) and Azerbaijan (9 km) (east)(see and read [7]) Turkey can be grouped under severalgeographical and socioeconomic regions such as the Balkans(Bulgaria Greece etc) (see and read [8]) the Caucasus

Hindawi Publishing CorporationAdvances in Decision SciencesVolume 2015 Article ID 548460 20 pageshttpdxdoiorg1011552015548460

2 Advances in Decision Sciences

Table 1 The peak load and the electricity consumption of Turkish Interconnected Electricity System

Year Peak load (MW) Percent change () Electricity consumption (GWh) Percent change ()1996 15231 75 94789 1081997 16926 111 105517 1131998 17799 52 114023 811999 18938 64 118485 392000 19390 24 128276 832001 19612 11 126871 minus112002 21006 71 132553 452003 21729 34 141151 652004 23485 81 150018 632005 25174 72 160806 722006 27594 96 174637 862007 29249 60 190000 882008 30517 43 198085 432009 29870 minus21 194079 minus202010 33392 118 210434 842011 36122 82 229319 90Data and source [14 15]

2530354045505560657075

050

100150200250300350400450500550600650700750800

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2011

Mill

ions

Billi

ons

GDP (current US$)Midyear population

Figure 1 GDP gross domestic product and population in Turkey(generated by the Microsoft Office Excel 2007)Data GDP (currentUSD 1961ndash2012) [12] (left axis) midyear population estimations(1961ndash2012) [13] (right axis)

Region (Azerbaijan Georgia etc) (see and read [9]) theEurope (France Germany etc) (see and read [10]) andthe MENA Region (Middle East and North Africa EgyptMorocco etc) (see and read [11]) This geographical locationalso gives an advantage to Turkey to interconnect its nationalelectricity grid to the other national electricity grids whichalso increases very much the importance of the currentsubject of this experimental research study not only for theperspective of Turkey but also for the perspective of theregions such as the Balkans the Caucasus and the MENA

The Turkish electricity generation establishments can begrouped according to their management styles organizationstructures sizes and business capabilities The diversifiedcharacteristics and properties of these entities in the Turkishelectricity generation market make the business and man-agement models and organizations classification study not

so difficult The decision making process of these entities aredifferent from each other based on these characteristic differ-ences The application and adaptation of several appropriatescientific methods are very important for some entities sothat the more the research studies by the different approachesand methods are conducted in this subject the more theappropriate scientificmethods and approaches will be startedto be used and preferred in the decision making process ofthe private small hydropower plant investments (PSHPPIs)in the practical daily life which will expectedly increase thetotal satisfaction on the PSHPPIs of all of the participants theparties and the involvers

The entities or the investors in the Turkish electricitygeneration sector can either invest in the renewable energysources (RESs) main group or in the fossil fuels sources maingroup The hydropower and the wind power in the RESsmain group and the natural gas and the imported coal in thefossil fuels main group have the major pie or share groups inthis market The projected installed capacity by the primaryenergy resources is presented in Figure 2

The hydropower plants are grouped as one segment with-out considering their installed capacities (each power plant)in this projection Figure 2 shows that the total percentageor share of the installed capacity of the hydropower plantsin Turkey shall be increased or tried to be increased toalmost 40 of the total installed power of the whole powerplants in Turkey until 2020s which indicates and means thatthe subject of this experimental research study will keep itsimportance in the short to long terms and periods Generallythe hydropower plants are classified based on their installedcapacities (119875) as large medium small mini- micro-and picohydropower plants However the consensus on theinstalled capacities of this classification has not been achievedyet For instance the SHPP installed capacity (kW) waspresented as (119875 lt 10000) by Dragu et al [33] (119875 lt 10000)by EREC [34] (1000 lt 119875 le 10000) by ESHA [35]

Advances in Decision Sciences 3

05

1015202530354045

Lignite + hard coal + imported coal Fuel oil+ otherNatural gas Nuclearbiogas + geothermal + waste + wind Hydro

2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

2021

Figure 2 Projected installed capacity (average of scenarios 1 and2) in Turkey ( of MW) (generated by the Microsoft Office Excel2007) Data [14 15]

(2000 lt 119875 le 25000) by Mishra et al [36] and (3000 lt

119875 le 25000) by Ramachandra and Shruthi [37]In the current study the SHPPs were accepted as

the hydropower plants that had the installed capacity of1000 kW lt 119875 le 10000 kW The EMRArsquos (Republic ofTurkey Energy Market Regulatory Authority) official website(httpwwwemragovtr or httpwwwepdkgovtr) hadbeen visited several times before this experimental researchstudy was started There were 212 SHPPs with the totalinstalled electrical power of 1048MWe until September 2012under the investigation and evaluation stage of the licenseapplication procedure (see Figure 3 for the SHPPsrsquo applica-tions to EMRA cumulative by year) The foreign domesticand local private investors (foreign investors from all overthe world such as Austria Norway and England domesticinvestors fromTurkey local investors fromArtvin) were ableto investigate select invest and have in their SHPPI portfolio(some of the megawatts) from the PSHPPI alternatives asshown in Figure 3

The presented data and the socioeconomic conditionsprove and show the reasons why the investors have searchedfor the private SHPP investments (PSHPPIs) as the long termreal sector investment alternatives Small to large size privateinvestors (establishments or real people) with different strate-gic investment plans have tried to find the PSHPPIs for havingsome or whole of the shares Some of the investors have alsolooked for several numbers of PSHPPIs to have them as onegroup

In this respect the main objective and the main problemof the private investors that should be solved in the mostappropriate convenient simple and understandable ways(please keep in mind that there may be several ways notonly one way) for the private investors are to find and selectthe most satisfying PSHPPIs on the point of view of theprivate investorsrsquo (in a more scientifically clear clause orstatement the decision makers of the private investors or theprivate investors by themselves) understanding perceptionand character amongst the possible alternative PSHPPIs For

Installed power (mechanical power) (MWm)

020406080

100120140160180200220240

2005 2006 2007 2008 2009 2010 2011 2012

Installed power (electrical power) (MWe)

Figure 3 SHPPsrsquo applications to EMRA (Latest 2012 September)(generated by the Microsoft Office Excel 2007) Data [14] (onlyofficial website)

instance the intentions of the different private investors (aprivate investormay be an institutional investor a legal entitya national or international joint venture and a single naturalperson or a group of them) are very different from each other(for instance the net profit maximization in the short termor the risk minimization in the long term) that makes themto take into account and consideration very different factorsduring the solution of the finding and selection problem ofthe PSHPPIsThemain aimof this study is to contribute to thescientific studies by defining the PSHPPIsrsquo selection problemand presenting an experimental research for its solutions

In this paper a private SHPPsrsquo investment selection prob-lem in Turkey was solved by mainly help of the ELECTRE(Elimination and Choice Translating Reality Elimination EtChoix Tradusiant la Realite) methods (one of the Multicrite-ria Decision Making (MCDM) methods) The objective andsubjective weighting methods were adopted for the decisionof the criteria weights or the voting power of the factors onlyIn the current experimental research case study there werefive private SHPP alternative investments (PSHPPIs) whichthe titles were not presented because of the possibility ofthe continuity of their commercially sensitive situations inTurkey However the sufficient data and information werepresented for the readers to make them understand theexperimental research case very well

This paper consists of four sections The methods arepresented by the literature review in the next section Theexperimental research case study is explained and the exper-imental research case study results are given in the thirdsection Finally the conclusions and future research arediscussed and presented in Section 4

2 Materials and Methods

The previous studies in the literature were reviewed in theexplicated twofold framework as presented in Figure 4

The previous studies in the first fold framework werereviewed on some scientific online database websites (allfieldsrsquo option selected) by help of the selected keywords untilthe 1st of January in 2014 The literature review in the first


Literature review framework

Literature review for thecore topic

Literature review for the lateralexpansion of the core topic

Keywords Keywords

(A) ELECTRE III(B) ELECTRE IV(C) ELECTRE III and small hydro(D) ELECTRE IV and small hydro(E) Shannonrsquos entropy(F) Subjective weighting(G) ELECTRE III and Shannonrsquos entropy(H) ELECTRE III and subjective weighting(I) ELECTRE III and Shannonrsquos entropy and small hydro(J) ELECTRE III and subjective weighting

and small hydro

(A) PROMETHEE and small hydro(B) QUALIFLEX and small hydro(C) ORESTE and small hydro(D) ARGUS and small hydro(E) EVAMIX and small hydro(F) MELCHIOR and small hydro(G) MAPPAC and small hydro(H) PRAGMA and small hydro(I) IDRA and small hydro(J) PACMAN and small hydro

Until the 1st of January 2014 Added during the revision until the 12th ofNovember 2014

Figure 4 The literature review framework of the current experimental research study (generated by the Apache OpenOffice 410 Draw)

Table 2 Summary of the literature review in the first fold framework

Scientific publisher Key terms(A) (B) (C) (D) (E) (F) (G) (H) (I) (J)

ACMDL 112 16 0 0 630 53 1 1 0 0ASCEOR 17 1 0 0 30 35 0 0 0 0ASME 2 0 0 0 25 3 0 0 0 0CJO 3 0 0 0 35 35 0 0 0 0DOAJ 21 6 0 0 11 1 0 0 0 0EI 6 0 0 0 7 10 0 0 0 0SD 416 69 8

lowast 0 1156 448 2 10 0 0TFJ 84 21 1

lowast 0 2 116 0 1 0 0WB 75 18 0 0 329 456 1 0 0 0WSP 14 5 0 0 175 12 0 11 0 0Data and source ACM Digital Library (ACMDL) (httpdlacmorg) ASCE Online Research Library (ASCEOR) (httpascelibraryorg) ASME(httpasmedigitalcollectionasmeorg) Cambridge Journals Online (CJO) (httpjournalscambridgeorg) DOAJ (httpdoajorg) Emerald Insight (EI)(httpwwwemeraldinsightcom) Science Direct (SD) (httpwwwsciencedirectcom) Taylor amp Francis Journal (TFJ) (httpwwwtandfonlinecom)Wiley-Blackwell (WB) (httponlinelibrarywileycom) and World Scientific Publishing (WSP) (httpwwwworldscientificcom)Keywords (A) ELECTRE III (B) ELECTRE IV (C) ELECTRE III and small hydrolowast (aim and scope difference with the current study) (D) ELECTRE IVand small hydro (E) Shannonrsquos entropy (F) subjective weighting (G) ELECTRE III and Shannonrsquos entropy (H) ELECTRE III and subjective weighting (I)ELECTRE III and Shannonrsquos entropy and small hydro and (J) ELECTRE III and subjective weighting and small hydro

fold framework showed that this paper would most probablybe one of the first studies in its aim and scope (see Table 2)

The previous studies in the second fold framework werereviewed on the same scientific online database websiteswith the same search options by help of the new selectedkeywords until the 12th of November in 2014 The keywordsor key phrases included the set of the other outrankingmethods such as the PROMETHEE (Preference Ranking

Organization METHod for Enrichment Evaluations) theQUALIFLEX (QUALItative FLEXible) the ORESTE (Orga-nization Rangement Et Synthese De Donnes Relationnelles)the ARGUS (Achieving Respect for Grades by Using ordinalScales) the EVAMIX (Evaluation of Mixed Criteria) theMELCHIOR (Methode drsquoELimination et de Choix Incluantles relation drsquoORdre) the MAPPAC (Multicriterion Analysisof Preferences by Means of Pairwise Actions and Criterion


Table 3 Summary of the literature review in the second fold framework


ACMDL 0 0 0 0 0 0 0 0 0 0ASCEOR 0 0 0 0 0 0 0 0 0 0ASME 0 0 0 0 0 0 0 0 0 0CJO 0 0 0 0 0 0 0 0 0 0DOAJ 0 0 0 0 0 0 0 0 0 0EI 0 0 0 0 0 0 0 0 0 0SD 21

lowast 0 2

lowast

15

lowast 0 3

lowast 0 2

lowast 0 0TFJ 1

lowast 0 0 1

lowast 0 1

lowast 0 0 0 0WB 1

lowast 0 1

lowast 0 0 0 0 0 0 0WSP 0 0 0 0 0 0 0 0 0 0Data and source ACM Digital Library (ACMDL) (httpdlacmorg) ASCE Online Research Library (ASCEOR) (httpascelibraryorg) ASME(httpasmedigitalcollectionasmeorg) Cambridge Journals Online (CJO) (httpjournalscambridgeorg) DOAJ (httpdoajorg) Emerald Insight (EI)(httpwwwemeraldinsightcom) Science Direct (SD) (httpwwwsciencedirectcom) Taylor amp Francis Journal (TFJ) (httpwwwtandfonlinecom)Wiley-Blackwell (WB) (httponlinelibrarywileycom) and World Scientific Publishing (WSP) (httpwwwworldscientificcom)Keywords (A) PROMETHEE and small hydrolowast (aim and scope difference with the current study) (B) QUALIFLEX and small hydro (C) ORESTE and smallhydrolowast (aim and scope difference with the current study) (D) ARGUS and small hydrolowast (aim and scope difference with the current study) (E) EVAMIX andsmall hydro (F) MELCHIOR and small hydrolowast (aim and scope difference with the current study) (G) MAPPAC and small hydro (H) PRAGMA and smallhydrolowast (aim and scope difference with the current study) (I) IDRA and small hydro and (J) PACMAN and small hydro

Comparisons) the PRAGMA (Preference RAnking Globalfrequencies in Multicriteria Analysis) the IDRA (Intercri-teria Decision Rule Approach) and the PACMAN (Passiveand Active Compensability Multicriteria Analysis) (see theoutranking methods in [38]) The literature review in thesecond fold framework presented that this paper wouldmost probably be one of the first studies in the usageand application of the outranking methods for solving theproblem explained in this study (see Table 3) which oughtto have encourage to work on these presented outrankingmethods in Table 3 in the future research studies

The first ELECTRE (ELimination Et Choix Traduisantla REalite ELimination and Choice Expressing the REality)method (ELECTRE I electre one) which was founded onthe outranking approach (the European school approach)was proposed in the 1960s by Bernard Roy (the inventor ofthe family of ELECTRE methods) (1934-alive by November2014) who was the founder of the LAMSADE and theresearchers at the European consultancy company SEMA(Societe drsquoEconomie et de Mathematiques Appliquees)(British and French information technology merger) (seealso LAMSADE (Laboratoire drsquoAnalyse et Modelisation deSystemes pour lrsquoAide a la DEcision httpwwwlamsadedau-phinefr) in France [39] Afterwards new versions of thismethod were evolved [39 40] The ELECTRE Iv (electreone vee) added a veto threshold into the method and theELECTRE IS (electre one esse) dealt with the imperfect data[40]TheELECTRE II (electre two)was developed for solvingthe problems of ranking actions [40 41] The ELECTRE III(electre three) was introduced as a more developed one usingthe pseudocriteria (the thresholds 119902

119895and 119901

119895 the imprecision

and the uncertainty) instead of the true-criteria (the smallestdifference in performancesmakes a strict preference betweenthe comparisons of the alternatives) and the fuzzy binary

outranking relations for ranking actions [40 42 43] TheELECTRE IV (electre four) was developed to deal with theproblems without working on the relative criteria importancecoefficients (unwillingness to present information on the roleof the criteria) [40 41 44] The ELECTRE TRI (electre tree)the ELECTRE TRI-B the ELECTRE TRI-C the ELECTRETRI-NC and the ELECTREGMS were the latest ELECTREmethods [41 44] The ELECTRE III [38 40ndash45] and theELECTRE IV [38 40 41 44] methods are based on thefollowing principles

The alternatives or actions or options with only partiallyknown a priori are 119860 = 119886

1 119886

2 119886

119894 119886

119898 where 119898 is

potential finite number of alternatives or actionsThe family of defined pseudocriteria is 119865 = 119892

1 119892

2

119892

119895 119892

119899 where 119899 ge 3

The performance of actions or alternatives 119886

119894on the

pseudocriterion 119892

119895is 119892119895(119886

119894) for all 119886

119894isin 119860 and 119892

119895isin 119865

The binary outranking relations are I (indifference reflex-ive and symmetric relation)P (strict preference nonreflexiveand asymmetric relation) Q (weak preference (hesitation)nonreflexive and asymmetric relation) andR (incomparabil-ity nonreflexive and symmetric relation) The partial binaryoutranking relations are shown in Figure 5

119902

119895is the indifference threshold 119901

119895is the preference

threshold and V119895is the veto threshold with respect to the 119895th

criterion (V119895

ge 119901

119895ge 119902

119895 for maximization criteria and for

minimization additive inverse)The researchers and the readers should be aware of the

difficulties of choosing the realistic threshold values in theELECTRE methods [46]

119902

119895is the highest value that beyond this value the difference

is clear for the human perception [46]119901

119895may be selected as at least twice as 119902

119895for a case that is

the symmetrical about the mean value [46]


hArr

hArr

hArr

|gj (ak) minus gj (an)| le qj forall(ak an) isin A

forall(ak an) isin A



ak anak an

ak an

ak an

ak an

or

akPj an (ak is strictly preferred to an)

akQj an (ak is weakly preferred to an)

akRj an (ak is incomparable to an)

gj (ak) gt gj (an) + pj

qj lt gj (ak) minus gj (an) le pj

Otherwise

is indifferent to an)akIjan (ak

Figure 5

V119895may be selected as at least three times as 119901

119895[46]

The voting power of 119892119895is 119908

119895and sum

119895|119892119895isin119865

119908

119895= 1 (1)

The group of the strict preference relation the weak pref-erence relation and the indifference relation is the partialbinary outranking relation 119878

119895= 119875

119895cup 119876

119895cup 119868

119895(≻119895= 119876

119895cup 119875

119895)

The comprehensive outranking relation is 119878 = 119875 cup 119876 cup 119868

(≻= 119876 cup 119875)

akSan and not (anSak)

(ak ≻ an) lArrrArr (ak is preferred to an)

forall (ak an) isin 119860

anSak and not (akSan)

(an ≻ ak) lArrrArr (an is preferred to ak)


akSan and anSak

akIan lArrrArr (ak is indifferent to an)


not (akSan) and not (anSak)

akRan lArrrArr (ak is incomparable to an)


(2)

The concordance index (the strength of the positive argu-ments) of the actions or the alternatives (ak an) (the valuesof concordance matrix) is

119888

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus 119902

119895

lt 1

if 119892119895(119886

119899) minus 119901

119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119902

119895

1 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119902

119895

(3)

The total or overall or global or comprehensive concordanceindex is

119862 (119886

119896 119886

119899) =

sum

119899

119895=1119908

119895times 119888

119895(119886

119896 119886

119899)

sum

119899

119895=1119908

119895

(4)

where 119908

119895is the weight of the criterion

The discordance index (the strength of the opposition) ofalternatives (119886

119896 119886

119899) is

119889

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus V119895

lt 1

if 119892119895(119886

119899) minus V119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119901

119895

1 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus V119895

(5)


The creditability or the credibility or the credit degree120590

119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)

The network relation in the ELECTRE IIIIV methods isbased on 120590

119904(119886

119896 119886

119899) ge 120582

The 120582 is called as the cut level and calculated by thehighest credibility index and the discrimination threshold If120590

119904(119886

119896 119886

119899) is above the 120582 cut level (050 le 120582 le 100 often

120582 = 067) then 119886

119896outranks 119886

119899 The 120582-strength and the 120582-

weakness is calculated for the ranking procedureThe rankingis based on the descending distillation (from the best to theworst) and the ascending distillation (from the worst to thebest) The qualification is gathered by these calculations Thefinal ranking can be found by the average of distillation chains[47]

There are four levels of binary outranking relations inthe ELECTRE IV method as the quasidominance relation(119878119902) the canonical-dominance relation (119878

119888) the pseudodom-

inance relation (119878119901) and the veto-dominance relation (119878V) (in

some improved ones the subdominance relation (119878119904) is added

as the fifth relation) [48 49] The ELECTRE IV is not theform of ELECTRE III with the equal criteria weights Thealgorithm of the ELECTRE IV method is as follows [49 50]

119898

119901(119886

119896 119886

119899) the number of criteria for which 119886

119896is

strictly preferred to 119886

119899

119898

119902(119886

119896 119886


119896is

weakly preferred to 119886

119899

119898

119894(119886

119896 119886


119896is

indifferent to 119886

119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886

119896) the number of criteria for

which 119886

119896has the same evaluation to 119886

119899

For any pair of alternatives (119886119896 119886

119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)

where119898 is the total number of criteria Consider

119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899

0 if no relation amongs 119878

119902 119878

119888 119878

119901 119878V

(8)

There are several objective weight assessment methodssuch as the extreme weight approach the random weightapproach and the entropy methods [51] One of the mostappropriate applicable methods is presented as the entropymethods amongst the objective weight assessment methods[51] There are some criticisms about the entropy methodsrsquocloseness to the true weight vector according to the mul-tiplicative error and the additive error when the decisionmakersrsquo decisions are based on the exponential scale [52]Despite these criticisms Shannonrsquos Entropy [53] (ShannonInformation by Claude Elwood Shannon so called ldquothefather of information theoryrdquo) (1916ndash2001) as below amongstseveral developed entropy methods such as De Luca andTermini Szmidt and Kacprzyk [54] was used for the criterionweight assessments in this experimental research studyShannonrsquos Entropy method was specifically preferred to beused adopted and investigated in the current experimentalresearch study to understand the nature and performanceof this objective weight assessment method for solving thedefined problem in this experimental research study and toobserve and predict its adoptability and its usage possibilityin the future more sophisticated models (on the researchdevelopment and deployment edge the computer basedintelligent decision making system and the autonomousdecision making systems) for the real world cases Themethod is shortly as follows [54ndash57]

The initialized decision matrix is 119883 = (119909

119894119895)

119899times119898

where 119894 isfor the criteria (1 le 119894 le 119899) and 119895 is for the alternative (1 le 119895 le

119898)The normalized matrix is 119877 = (119903

119894119895)

119899times119898

The elements of the normalized matrix 119903

119894119895take the values

between 0 and 1 where

119903

119894119895=

119909

119894119895minusmin

119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895

(for the criterion which is a kind of maximization)

119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895

(for the criterion which is a kind of minimization)

(9)


The entropy is 119890119894(note in general119867119867(119901(119909) or119867(119860))) of the

119894th criterion as

119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0

the weight of entropy of 119894th criterion as 119908

119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)

The subjective criteria weighting by Saatyrsquos AHP (AnalyticHierarchy Process byThomas L Saaty) (1926-alive byNovem-ber 2014) that was based on the pairwise comparisons ofthe criteria the geometric mean approximation and thenormalization [58ndash60] was also used for the criterion weightassessments in this experimental research study Saatyrsquos AHPmethod (as for the subjective weight assessment method)was especially chosen to be employed and applied in thisexperimental research study because of its capability oftaking the expertsrsquo thoughts in a free and scientific wayaccording to the expertsrsquo experiences and preferences

Despite the ELECTRE methods have the main recom-mendation of being applied up to thirteen criteria it isbelieved that the current experimental research case study(seventeen criteria) can also be handled with ease by theELECTRE methods

The ELECTRE III (for ranking decision) the ELECTREIV (for ranking decision) Shannonrsquos Entropy (for votingpower decision) and Saatyrsquos AHP subjective criteria weight-ing (for voting power decision) methods were applied andtested in the experimental research case study as presentedin the next section

3 The Experimental Research Model CaseResults and Discussion

The ELECTRE methods are very effective for solvingthe problems with large number of actions or alterna-tives [38ndash46] However only five candidate private SHPPinvestments in the predevelopment investment stages wereinvestigated during this experimental research case studyThe data and information of these candidate PSHPPIswere collected and evaluated according to ten subjectiveand seven objective criteria The experimental researchmodel was built and performed by both Microsoft Excel(httpwwwmicrosoftcom) and Apache OpenOffice Calcsoftware (httpwwwopenofficeorg) The model files of theexperimental research case study in lowastxls and lowastods formatswere also available for the readers (correspond and contact tothe author and also see the electronic supplementary mate-rial) Moreover it should be mentioned that the electrical

installed capacity 119875 (in Watts W) (see and read [61]) of aSHPP was calculated by the following formula

119875 = 120578tr times 120578

119892times 120578

119905times 120588

119908times 119892 times 119876 times 119867 (11)

where 120578tr is efficiency of transformer 120578

119892is efficiency of

generator 120578119905is efficiency of turbine 120588

119908is density of water

(kgm3) 119892 is gravity (ms2) 119876 is designproject discharge(m3s) and 119867 is net head (m) (J Joule kg kilogram mmeter N Newton s second W Watt) (W = Js = N lowastms =

kg lowast m2s3) (for extraction of this formulaequation see andread [18 62 63])

The criteria in the current experimental research studywere selected as given in Table 4 based on the state of mindin the positive thinking (please look for the state of mind andthe positive thinking terms see and read [64ndash68])

The major concentration interest effort and workinghours (spent hours) in this experimental research studywas not mainly spent on finding defining identifyingdescribing and selecting the PSHPPIsrsquo selection factors orcriteria instead the main focus and the core research interestof the current experimental research study were applying andtesting the mentioned and noticed methods observing anddeeply understanding their ability capability and usabilityand analyzing their performance on reflecting the decisionmakers preferences and opinions on the selection of thePSHPPIsrsquo problem area learning their difficulties for thefuture real world applications (very large number of criteriasets and actions sets) and solving this experimental case prob-lem Henceforth the criteria or factors on this experimentalresearch model were found gathered and selected from theprevious research studies of the author (please correspond toand contact to the author from the presented e-mail addressto get more information about those previous researchstudies (publishedunder reviewunder revisions reviewyetunpublished stages) on those subjects) The objective criteria(Cr criterion) in this experimental research study were suchas the catchment area (Cr01) which was taken into accountin the current experimental model because it was one ofthe important elements that could be affected by the climaticconditions and at the same time influenced the projectrunoff and the flow rate the project runoff (Cr02) that wasconsidered in the current experimental model because itshowed the water flown over the earthrsquos surface generatedmainly by the rainfall and the snow and affected the flowrate the net head (Cr03) that was examined in the currentexperimental model because it was one of the items thatdefined the types of the electromechanical equipment andtheir operation conditions and at the same time it was a directvariable of the installed capacity and the electricity generationby the PSHPPs the flow rate (Cr04) which was studied in thecurrent experimentalmodel because it presented the amountof water that could be run through the water turbines at thedefined specific duration and at the same time it was a directvariable of the installed capacity and the electricity generationby the PSHPPs the firm energy (Cr05) and the secondaryenergy (Cr06) that were taken into account in the currentexperimental model because they determined directly thegross income or the earnings (so that the net income) of the


Table 4 The criteria description

Crlowast Criterion SOMlowastlowast MM+ S Description

Objectivecriteria

Cr01 Catchment area(km2) nc ma n

The approximate numerical value was taken frominformation form (General Directorate of State HydraulicWorks httpwwwdsigovtr) of the SHPP (for the term [16])

Cr02 Project runoff(hm3) nc ma n The approximate numerical value was taken from

information form (for this term [17])

Cr03 Net head (m) nc ma n The approximate numerical value was taken frominformation form (for this term [16])

Cr04 Flow rate (m3s) nc ma n The approximate numerical value was taken frominformation form (for this term visit [16])

Cr05 Firm energy(GWh) nc ma n

Tthe power delivered during a certain period of the day withat least 90ndash95 certaintyrdquo [18] The approximate numericalvalue was taken from information form

Cr06 Secondaryenergy (GWh) nc ma n The approximate numerical value was taken from

information form

Cr07 Investment cost(million USD) nc mi n

The approximate numerical value was taken frominformation form The total estimated investment cost was inUS Dollars The exchange rate was taken from the CentralBank of the Republic of Turkey (httpwwwtcmbgovtr) on8th of September in 2013

Subjectivecriteria

Cr08 River basin ptd ma ls The main river basins of the projects were evaluated by theEDMs based on their knowledge and experience

Cr09 Conveyancestructure ptd ma ls

The conveyance structures of the SHPP projects wereevaluated according to the knowledge and the experiences ofthe EDMs (for this term [19])

Cr10 Communityattitude ptd ma ls The local community supportive or opposition opinion about

the SHPPs was investigated in this criterion

Cr11 Transportation ptd ma lsThe availability flexibility quality and conditions of all thetransportation modes were evaluated by the EDMs based ontheir knowledge and experience

Cr12 Topography ptd ma ls The surface shapes and features of SHPPsrsquo site were evaluatedby the EDMs

Cr13 Geology ptd ma ls The geological conditions and properties of SHPPsrsquo site wereevaluated by the EDMs

Cr14 Securityconditions ptd ma ls

The public security the infrastructure security and othersecurity groups were evaluated based on the theft theburglary and other security risks and threats (see [20 21]) bythe EDMs

Cr15 Terrorismconditions ptd ma ls The perceived terrorism risks and threats (see [22 23]) were

evaluated by the EDMs

Cr16 Protected areas ptd ma ls The natural parks the ecological values and so forth wereevaluated by the EDMs

Cr17 Substationconditions ptd ma ls The conditions of the grid connection were evaluated by the

EDMslowastCr code lowastlowastSOM state of mind nc no condition because of objective criteria ptd positive thinking direction +MM maximizationminimization mamaximization mi minimization S scale n numerical scale ls 5-point Likert scale 1 to 5 the worst to the best and EDM expert decision makerSee and visit [24] for square kilometer (km2) [25] for cubic hectometer (hm3) [26] for meter (m) [27] for cubic metre per second (m3s) [28] for gigawatthour (GWh) [29] for million and [30] for USD

PSHPPs and finally the investment cost (Cr07) which wasevaluated in this experimental model so that the financial oreconomic performance of the PSHPPIs would be tried to beestimated by considering both the income (as a whole) andthe cost (as a whole) at the same time All of these criteriawere evaluated concurrently in the current experimentalmodel for not missing and omitting any important issuessubjects topics and points and at the same time for having

the consistent data and information set so that it aims tobe placed in the safe analysis and investigation actions oralternatives space for the electricity generation amount of thePSHPPIsThe subjective criteria in this experimental researchstudywere such as the river basin (Cr08) (for exampleMeric-Ergene River Basin Marmara River Basin and SusurlukRiver Basin in Turkey) which was studied in the currentexperimental model to put the characteristics and the future


Table 5 The PSHPPIs actions in this experimental case study

Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)

Cr07(Million USD) Cr09

A1 79 47 369 3 26 15 115 Channel closedrectangular 3900m

A2 61 48 388 3 6 31 78 uPVC pipe 3300m

A3 329 131 172 8 16 38 166 Channel openrectangular 9600m

A4 130 133 135 10 14 29 241 Tunnel modifiedhorseshoe 8800m

A5 553 701 97 195 29 23 279 Tunnel circular5900m

See and read [24] for square kilometer (km2) [25] for cubic hectometer (hm3) [26] for meter (m) [27] for cubic metre per second (m3s) [28] for gigawatthour (GWh) [29] for million and [30] for USD see read and watch [31] and see and read [32] for some issues about the conveyance structures

conditions and predictions of the river basins into thismodelthe conveyance structure (Cr09) (for example a long tunnela short tunnel an open channel and several tunnels) that waspreferred to be evaluated to try to foresee the difficulties andthe obstacles mainly during the construction period and theoperation period the community attitude (Cr10) which wasconsidered in the current experimental model for predictingthe supporting activities the oppositions the blockages andthe protests against the PSHPPI the transportation (Cr11)that was evaluated in this experimentalmodel for the difficul-ties before the construction period during the constructionperiod and during the operational period the topography(Cr12) which was put into the current experimental modelfor the difficulties and the easiness of the activities for theconstruction and the investigations and the engineering stud-ies before the construction period during the constructionand operational periods the geology (Cr13) which was takeninto account in the current experimental model because theactivities and all of the design and construction works wererelated with this factor the security conditions (Cr14) thatwas considered in this experimental model for predictingthe difficulties such as the security risks and threats forthe private life the public life and the infrastructure beforethe construction period and during the construction andoperational periods the terrorism conditions (Cr15) thatwere taken into account because of the same reasons with thesecurity conditions but with a devastating effect such as thecivil disorder the political the nonpolitical the ideologicaland the official or state terrorisms the protected areas (Cr16)(for example the cultural values the natural parks theimportant bird areas and the rainforests) that was evaluatedfor predicting the permission works and also the communityattitude and at the same time for having environmentallyfriendly compatible and responsible PSHPPs and finally thesubstation conditions (Cr17) whichwas studied for analyzingthe connection to the grid possibilities and conditions beforeand during the construction period and the easiness and theability of the operation and the maintenance of the connec-tion lines during the construction period All of these criteriawere thought to be evaluated by the healthy honest fairreliable straightforward trustworthy and pragmatic experts

and decision makers (in other words not ill unhealthydishonest unfair unreliable unreasonable insincere anduntrustworthy) under the normal conditions (for instancenot under any duress coercion threat violence mobbingand bullying)

The actions or alternatives or options in the currentexperimental research study were found and taken fromthe PSHPPIs portfolio in Turkey (please consider thinkand imagine all of the private power plants in Turkey as awhole private investment portfolio set for the real sectorsrsquoforeign or domestic or local private investors moreoverplease keep in mind that the private small hydropower plantsinvestment set is a subset of this whole private investmentportfolio set) which could be accepted and assumed as freeor available or ready to be sold or exchanged some of itsshares and stocks in the predevelopment investment stagesThe main characteristics of these actions were gathered fromthe PSHPPIs official records on the open sources as some ofthem presented in Table 5

The experimental research model of the current studywas founded on the EDMrsquos preferences and evaluationshenceforth the main decision making process was supportedby the ELECTRE III (ranking) and Saatyrsquos AHP (votingpower) (imagine like the highway) the experimental decisionmaking process had threemain sections or parts (imagine likethe sideways) as the ELECTRE III (ranking) and ShannonrsquosEntropy (voting power) the ELECTRE III (ranking) and theEqual Weighting (voting power) and the ELECTRE IV Inaddition to these main sections (methods and approaches)three 120582 cut levels were used for the investigation and theanalysis of the discrimination and the distinction of theactions or the alternatives in this experimental research studyThe experimental researchmodel was tried to be presented bythe help of Figure 6

In the current experimental case study there were twoexperts who were also the decision makers (a group decisionmaking case) This condition made the use of the expertdecision maker (EDM) term possible The expert decisionmakers (EDM

1and EDM

2 multidisciplinary experts) were

capable of evaluating all of these criteria in a sufficientmannerTheEDMs took their weighting power (weight of the


120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria

Criteria Criteria classification

Catchment areaProjectrunoff

Net headFlow rate

Firm energySecondaryenergy Investment

cost

River basin

Community attitude

Conveyance structure

TransportationTopography

Geology

Terrorism conditions

Securityconditions

Protectedareas

Substation conditions

Actions(alternatives)

Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5

ELECTRE III(ranking)

Shannonrsquos entropy(voting power)

Note For all criteria and

alternatives

Note For all

methods


Saatyrsquos AHP(voting power)


equal weighting(voting power)

ELECTRE IV

Reflectance and comparision of voting power

Reflectance and comparison of voting power

Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of

discriminationResults

(same value but different graphics representation)

NoteAnalyze

experimentalresults

and makerecommendation

No decision evaluation

(quantitative)

Decision

evaluation(qualitative)

Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2

1A1 A2 A3 A4 A5 IIISE1

IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level

Figure 6 The experimental research model (generated by the Apache OpenOffice 410 Draw)

EDM) on the decision process by their practical experiencein the industry and the educational background (bachelormaster and doctoral degrees in the engineering fields)

The subjective criteria were evaluated by the Likert 5type scale (by Likert 1903ndash1981) [69] and the linguistic orverbal statements considering the basic principles of thehuman mind cognitive capacity such as the magical number7 7 plusmn 2 rule (by Miller (1920ndash2012) Shiffrin (1968-alive byNovember 2014) and Nosofsky (alive by November 2014))[70 71] and the verbal qualifiers (by Rohrmann (alive byNovember 2014)) [72] as presented in Table 6

The criteria weights were found by Shannonrsquos Entropymethod (objective weighting) and by Saatyrsquos AHP method(subjective weighting) as shown in Figure 7 The consistencyratios of the EDMsrsquo evaluations were found as 99 and97 respectively in Saatyrsquos AHP method for the criteriaweighting which were less than 10 and in the acceptablelevels Shannonrsquos Entropy method calculated the highestpriority for the project runoff the catchment area theflow rate and the community attitude criteria respectivelyThe EDMs gave the highest priority to the terrorism thesubstation and the security respectively as calculated bySaatyrsquos AHP method for the criteria The difference of thevalues between Shannonrsquos Entropy and Saatyrsquos AHP methodfor the project runoff the catchment area the flow ratethe community attitude the terrorism the substation andthe security criteria were 01193 (EDM

1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419

(EDM1) and minus01418 (EDM

2) minus01111 (EDM

1) and minus01235

(EDM2) minus01038 (EDM

1) minus00864 (EDM

2) respectively

These experimental results showed that Shannonrsquos Entropymethod was not able to reflect exactly the EDMsrsquo perceptionon the criteria calculated by Saatyrsquos AHP method in this par-ticular experimental case (Figure 7) (note important findingfor this experimental research model and this experimentalresearch case)

The EDM1took the weight of 04 and the EDM

2took

the weight of 06 by the agreed upon point of view and theconsensus of the EDMs because of being not only basedon their experience and knowledge on the PSHPPIs butalso according to their specific and particular interest atten-tion consideration focus and examination on the currentexperimental research case The evaluations for all criteria ofthe EDMs were compared and checked with each other aspresented in Figure 8

The performance of the alternatives the indifferencethresholds the preference thresholds the veto thresholdsand the criterion weights of criteria for the EDMs and thepercentage of the differences of these performances thresh-olds weights and the characteristics of the EDMs made theaggregation process sufficiently acceptable and possible by(12) and (13) as the IDAMS (Internationally Developed DataAnalysis andManagement Software) of theUNESCO(UnitedNations Educational Scientific and Cultural Organization)(see some issues for the principle approaches [73ndash82])


000 004 008 012 016 020

Catchment areaProject runoff

Net headFlow rate

Firm energySecondary energy

Investment costRiver basin

Conveyance structureCommunity attitude


GeologySecurity

TerrorismProtected areas

Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2

Shannonrsquos entropy (voting power)

Saatyrsquos AHP (voting power)

Reflectance of Shannonrsquos entropy for Saatyrsquos AHP (comparison of voting power)


Net headFlow rate





GeologySecurity


Substation

Figure 7 The objective and the subjective criteria evaluations by the EDMs (generated by the Microsoft Office Excel 2007)


Table 6 The subjective criteria evaluation by the EDMs

Subjective criteria Actions (alternatives)Code Name Direction of preference A1 A2 A3 A4 A5

Expert decision maker 1 (EDM1)

Cr08 River basin Max VB G B VG VGCr09 Conveyance structure Max G VG A VB BCr10 Community attitude Max A B G VB VBCr11 Transportation Max VG B A G GCr12 Topography Max VG B A G GCr13 Geology Max G B VB A ACr14 Security conditions Max VG G B G ACr15 Terrorism conditions Max VG A VB G GCr16 Protected areas Max B A VG G GCr17 Substation conditions Max B G A A A


Cr08 River basin Max VB G B VG VGCr09 Conveyance structure Max G VG A VB BCr10 Community attitude Max A B G VB VBCr11 Transportation Max VG B A G GCr12 Topography Max VG B A G GCr13 Geology Max G B VB A ACr14 Security conditions Max VG G B A ACr15 Terrorism conditions Max VG A VB A GCr16 Protected areas Max B A VG G GCr17 Substation conditions Max B G A A ALinguistic or verbal statements(5) VG very good (4) G good (3) A average (2) B bad (1) VB very bad

The threshold values were defined based on the principlesexplained in the previous section as in Table 7 Consider

The concordance index 119888119895(119886

119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)

where 119911 indicates the experts as 119885 = 119911

1 119911

2 119911

119894 119911

119910119910

Consider

The weight of the criterion 119908119895=

sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911

The discordance index 119889119895(119886

119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)

In the current experimental case study the experimentalmodel was built upon the consideration of the main featuresthe criticisms the improvements and the new approaches forthe ELECTRE methods (see [44]) The credibility (degree)matrices of the ELECTRE III with the objective weighting(Shannonrsquos Entropy) the ELECTRE III with the subjectiveweighting (Saatyrsquos AHP) the ELECTRE III with the EqualWeighting and the ELECTRE IV were calculated and pre-sented as shown in Table 8

The 120582 cut level was first selected as (120582 = 067) then (120582 =

085) and (120582 = 090)

The decending distilation process and the ascendingdistilation process (upward and downward distilation) werecalculated from the credibilitymatrices by the help of the sumof the elements of each row and the sum of the elements ofeach columnThe sum of the elements in each row presentedthe strength of the criterion and the sum of the elements ineach column showed theweakness of the criterionThe calcu-lations were also checked by the help of the relation graphs asshown in Figures 9 and 10 (see the electronic supplementarymaterial in the Supplementary Material available online athttpdxdoiorg1011552015548460 for the whole details ofthe calculations)

The ranks for each method and for each 120582 cut level weregathered to make the final decision and to deeply understandand analyze the nature of the methods and the approachesin the current experimental research study as presented inTable 9

The ELECTRE III (ranking) with Shannonrsquos Entropy(voting power) in the 067 120582 cut level gave the preference ofthe PSHPPIs (the rankings of the actions or the alternatives)as Action or Alternative 5 in the first rank Action 1 Action 2Action 3 andAction 4 in the second rankThediscriminationor separation or partition in this experimental case was notdefinite or distinct as only two preference or selection or ranksets (1 and 2) could be found in the results and findings Therankings of the PSHPPIs in the 085 120582 cut level were Actionor Alternative 5 in the first rank Action 2 and Action 3 in


0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

The indifference threshold for EDM1 and EDM2 The preference threshold for EDM1 and EDM2

The veto threshold for EDM1 and EDM2 The criteria weight for EDM1 and EDM2

EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj

Figure 8 The indifference threshold the preference threshold the veto threshold and the criteria weight of the EDMs (generated by theMicrosoft Office Excel 2007)

Network relation based on cut level (120582 = 085) for ELECTRE III (ranking) and the Shannonrsquos entropy (voting power)

S strength A1 A2 A3 A4 A5 S S W Q D A Final rankOutranking

relationAlternatives

Alte

rnat

ives

(act

ions

)W weakness 1 1 0 1 0 3 A1 3 5 4 3 3Q qualification 1 1 1 1 0 4 A2 4 4 0 3 1 2A ascending 1 1 1 1 0 4 A3 4 3 1 2 2 2D descending 1 1 0 1 0 3 A4 3 5 4 3 3

1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1

Descending distillation process

Ascending distillation process

A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2

Figure 9The descending distillation process and the ascending distillation process I (see the electronic supplementarymaterial for the wholedetails of the calculations)


Table 7 The threshold values

Criterion EDM1

EDM2

Indifference 119902

119895Preference 119901

119895Veto V

119895Indifference 119902


119895Veto V

119895

Cr01 130 260 780 100 200 600Cr02 80 160 480 60 120 360Cr03 170 340 1020 160 320 960Cr04 8 16 48 6 12 36Cr05 10 20 60 9 18 54Cr06 25 50 150 20 40 120Cr07 10 20 60 9 18 54Cr08ndashCr17lowast 2 3 5 2 3 5lowastSame value from Cr08 to Cr17

Table 8 The creditability or the credibility degrees and matrix for all methods

Methods Credibility matrices

ELECTRE III(ranking)Shannonrsquos Entropy(voting power)

A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000

ELECTRE III(ranking)Saatyrsquos AHP(voting power)

A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000

ELECTRE III(ranking)Equal Weighting(voting power)

A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

the second rank and Action 1 and Action 4 in the third rankThe discrimination in this one (120582 = 085) was more clearthan the previous one (120582 = 067) as three selection sets (12 and 3) could be found in the results and the findings Therankings of the PSHPPIs in the 090 120582 cut level were Actionor Alternative 5 in the first rank Action 1 and Action 3 inthe second rank Action 2 in the third rank and Action 4 inthe fourth rank The discrimination in this one (120582 = 090)was the most recognizable and definite one (120582 = 085 120582 =

067) as four selection sets (1 2 3 and 4) could be found inthe results and the findings All of the final rankings in the

current experimental research study are presented in Figure 11to give an a whole overview of the methods (for ranking andvoting power) and the ranks Action 5 was positioned in thefirst rank by all of the methods and 120582 cut levels accordingto the preferences (the indifference threshold the preferencethreshold the veto threshold and the criteria weight) of theEDMs in this experimental research case (see Table 9) Action1 was positioned in the second rank by all of the methods and120582 cut levels except the ELECTRE III (ranking) with ShannonrsquosEntropy (voting power) at the 120582 cut level of 085 and theELECTRE IV based on the preferences of the EDMs (see


Table 9 The ranks for each method and for each 120582 cut level

Methods 120582 cut level A1 A2 A3 A4 A5 Abbreviation on Figure 11

ELECTRE IIIShannonrsquos Entropy

067 2 2 2 2 1 IIISE1085 3 2 2 3 1 IIISE2090 2 3 2 4 1 IIISE3

ELECTRE IIISaatyrsquos AHP

067 2 3 4 3 1 IIISA1085 2 3 4 3 1 IIISA2090 2 3 4 3 1 IIISA3

ELECTRE IIIEqual Weighting

067 2 2 2 2 1 IIIEW1085 2 3 4 3 1 IIIEW2090 2 4 3 5 1 IIIEW3

ELECTRE IV067 1 1 1 1 1 IV1085 1 1 1 1 1 IV2090 1 1 1 1 1 IV3

Network relation based on cut level (120582 = 090) for ELECTRE III (ranking) and the Shannonrsquos Entropy (voting power)



Alte

rnat

ives

(act

ions

)W weakness 1 1 0 1 0 3 A1 3 2 2 2 2Q qualification 0 1 0 1 0 2 A2 2 3

13 3 3

A ascending 0 1 1 1 0 3 A3 3 2 1 2 2 2D descending 0 0 0 1 0 1 A4 1 5 4 4 4

1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5

Figure 10 The descending distillation process and the ascending distillation process II (see the electronic supplementary material for thewhole details of the calculations) (generated by the Microsoft Office Excel 2007)

Table 9) Action 2 was stood in the three highest two lowestand seven middle rank selection sets or classes Action 3had three highest ranks three middle ranks and six lowestranks Action 4 was included in three highest four middleand five lowest rank selection sets It was observed in thisexperimental research study that the ELECTRE IV was nothelpful for the discrimination or separation or partition ofthe current actions or alternatives under these preferences ofthe EDMs so that the ELECTRE IV could not be expressedor accepted as a responsive or sensible or sensitive methodin the current experimental research case The ELECTRE III(ranking) with Saatyrsquos AHP (voting power) method gave thesame ranks and classification (Action 5 1st Action 1 2nd

Action 2 and 4 3rd Action 3 4th) in all of the120582 cut levels (120582 =

067 120582 = 085 and 120582 = 090) These findings and explorationon the ELECTRE III Saatyrsquos AHP method showed that the 120582

cut levels did not make any difference in the results and thefindings of this experimental research case Moreover thisexperimental research study presented that the reflectanceof the ELECTRE III and Shannonrsquos Entropy method andthe ELECTRE III and the Equal Weighting method on theELECTRE III and Saatyrsquos AHPmethod got higher and highervalues while the 120582 cut levels got higher and higher values

The final rankings and the overall results were also finallydiscussed by the EDMs in the current experimental researchstudy and it was agreed upon thatAction orAlternative 5 then


IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3

Surface view of the final ranks of the ranking methods and the voting power for each 120582 cut level

Bar chart view of the final ranks of the ranking methods and the voting power for each 120582 cut level

AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2

Figure 11The final ranks of the experimental research case study (surface view generated by theMicrosoft Office Excel 2007 bar chart viewgenerated by the Apache OpenOffice Calc)

Action 1 took the highest ranks Action 3 took the lowest rankandAction 2 andAction 4 took themiddle ranksHenceforthAction or Alternative 5 and the Action 1 had to bemoved intothe development investment stages of the PSHPPIsThe otheralternatives had to be studied after these two PSHPPIs

4 Conclusions Future Applicationsand Research

In this experimental research study the solution of a privateSHPP projectsrsquo investment selection problem in Turkey wastried to be solved by the help of mainly the ELECTRE IIIIVmethods The EDMs tried to gather as much as supportfrom the scientific methods so that the criteria weightswere defined by two different methods as the ShannonrsquosEntropy and the Saatyrsquos AHP In addition to these calcu-lations the equal weight calculations for the ELECTRE IIIwere performed to increase the number of the experimentalmethods for a better analysis and investigation for thisexperimental research study and the future research studies(on the research development and deployment edge thecomputer based intelligent decision making system and theautonomous decision making systems) All of these studiesempowered the EDMs to express their ideas and made theirmind up in a correct manner The EDMs realized that thedecision on the value of the indifference threshold (119902

119895) the

preference threshold (119901119895) and the veto threshold (V

119895) was

very difficult and crucial Henceforth the special attentionshould be given to the evaluation of these thresholds in thefuture research studies

This experimental research study should be followed bythe evaluation of the thresholds study All of the thresholdsshould be reevaluated wherever necessary and the finaldecisions should be taken according to these renewed cal-culations In addition the current experimental case studyshould be performed based on only the subjective criteriaand only the objective criteria This study will show how thefinal decisions are generally affected by the subjective factorsMoreover the number of criteria and the combinations of cri-teria should be reorganized and a new study should be doneor performed Afterwards the studies should be performedfor the different project stages such as the development stagesin the small hydropower plant industry

These kinds of research studies most probably will helpthe investors the institutions organizations (internationaland domestic) and the governments to invest in the mostappropriate investments in the real sectors that will help touse the resources (financial manpower and mind power) asefficiently and effectively as possible Hence the appropri-ateness the suitability the convenience and the coherenceof these kinds of investment decisions in the real sectorscan surely affect impact and touch on the most positiveway to the upper most objectives of humankind such as


fighting against hunger and malnutrition prevention of andfight against crime keeping peace and security respectingfor justice and the rule of law preserving human rights andfreedom improving health and wealth status

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The author would like to deeply and sincerely thank Pro-fessor Dr Bernard ROY for his help to make the author tounderstand clearly the distinction between ELECTRE III andELECTRE IV methods and their respective results

References

[1] H Kemal Ozturk A Yilanci and O Atalay ldquoPast present andfuture status of electricity in Turkey and the share of energysourcesrdquo Renewable and Sustainable Energy Reviews vol 11 no2 pp 183ndash209 2007

[2] M Balat ldquoElectricity consumption and economic growth inturkey a case studyrdquoEnergy Sources Part B Economics Planningand Policy vol 4 no 2 pp 155ndash165 2009

[3] G Boluk and A A Koc ldquoDynamics of energy consumptionpatterns in Turkey its drivers and consequencesrdquo inProceedingsof the World Reneable Energy Congress on Sustainable Cities andRegions (SCR rsquo11) pp 3476ndash3483 Linkoping SwedenMay 2011

[4] Wikimedia FoundationWikipedia Turkey httpenwikipediaorgwikiTurkey

[5] G Friedman ldquoGeopolitical Journey Part 5 Turkeyrdquo StratforGlobal Intelligence httpwwwstratforcomweekly20101122geopolitical journey part 5 turkeyaxzz3IfqoHhmN

[6] Center for Strategic and International Studies (CSIS) ldquoSearchfor Turkeyrdquo httpcsisorg

[7] Wikimedia Foundation ldquoGeography of Turkeyrdquo WikipediahttpenwikipediaorgwikiGeography of Turkey

[8] Wikimedia Foundation Wikipedia Balkans httpenwiki-pediaorgwikiBalkans

[9] Wikimedia Foundation Inc Wikipedia Caucasus 2014httpenwikipediaorgwikiCaucasus

[10] Wikimedia Foundation Wikipedia Europe httpenwiki-pediaorgwikiEurope

[11] Wikimedia Foundation Wikipedia MENA Middle East andNorth Africa httpenwikipediaorgwikiMENA

[12] Worldbank ldquoThe data of the Gross Domestic Product (GDP)(current USD 1961-2012)rdquo 2013 httpwwwworldbankorg

[13] Turkish Statistical Institute ldquoThe data of the mid-year popula-tion estimations (1961ndash2012)rdquo httpwwwturkstatgovtr

[14] EMRA (Republic of Turkey Energy Market RegulatoryAuthority) ldquoThe data of the Turkish Electrical Energy 10-year Generation Capacity Projection 2012ndash2021 Reportrdquohttpwwwemragovtr httpwwwepdkgovtr

[15] TEIAS (Turkish Electricity Transmission Corporation) Thedata of the Turkish Electrical Energy 10 year GenerationCapacity Projection 2012ndash2021 Report httpwwwteiasgovtr

[16] EIA (US Energy Information Administration) httpwwweiagovtoolsglossary

[17] USGS (US Geological Survey) httpgawaterusgsgov[18] ESHA (European Small Hydropower Association) Guide on

How to Develop a Small Hydropower Plant Brussels Belgium2004

[19] IWA (IWAWaterWiki) September 2013 httpwwwiwawater-wikiorg

[20] Front Line Protection Manual for Human Rights DefendersFront LineThe International Foundation ForThe Protection OfHuman Rights Defenders Dublin Ireland 2005

[21] FreightWatch FreightWatch International 2013 httpwwwfreightwatchintlcom

[22] United Nations 2013 httpwwwunorgenterrorismindexshtml

[23] UNODC (United Nations Office on Drugs and Crime) 2013httpwwwunodcorg

[24] Wikimedia Foundation Inc Wikipedia square kilometer2014 httpenwikipediaorgwiki Square kilometre

[25] Wikimedia Foundation Wikipedia cubic hectometer 2014httpenwikipediaorgwikiCubic metreMultiples and sub-multiples

[26] Wikimedia FoundationWikipedia meter 2014 httpenwiki-pediaorgwikiMetre

[27] Wikimedia Foundation Wikipedia cubic meter per second2014 httpenwikipediaorgwikiCubic metre per second

[28] Wikimedia Foundation Wikipedia gigawatt hour 2014httpenwikipediaorgwikiKilowatt hour

[29] Wikimedia Foundation Wikipedia million 2014 httpenwikipediaorgwikiMillion

[30] Wikimedia Foundation Wikipedia United States dollarUSD US$ US dollar American dollar US Dollar 2014httpenwikipediaorgwikiMillion

[31] S A Kartha National Programme on Technology EnhancedLearning (NPTEL) Civil Engineering Courses AdvancedHydraulics Course 2014 httpnptelacincourses105103021

[32] Pipe Flow Software 2014 httpwwwpipeflowcompipe-flow-advisor-softwarechannel-flow-calculator

[33] C Dragu T Sels and R Belmans Small Hydro Power-State ofthe Art andApplications ESAT-ELEN Energy Institute LeuvenBelgium 2010

[34] EREC (European Renewable Energy Council) REN21 Renew-ables 2012 Global Status Report European Focus Paris France2012

[35] ESHA (European Small Hydro Association) Guide on Howto Refurbish Low Head Small Hydro Sites ESHA BrusselsBelgium 2010

[36] S Mishra S K Singal and D K Khatod ldquoA review onelectromechanical equipment applicable to small hydropowerplantsrdquo International Journal of Energy Research vol 36 no 5pp 553ndash571 2012

[37] T V Ramachandra and B V Shruthi ldquoSpatial mapping ofrenewable energy potentialrdquo Renewable and Sustainable EnergyReviews vol 11 no 7 pp 1460ndash1480 2007

[38] J Figueira V Mousseau and B Roy ldquoPart III outrankingmethodsrdquo inMultiple Criteria Decision Analysis State of the ArtSurveys J Figueira S Greco andM Ehrgott Eds pp 163ndash260Springer Boston Mass USA 2005

[39] W C Huang and C H Chen ldquoUsing the ELECTRE II methodto apply and analyze the differentiation theoryrdquo Proceedings ofthe Eastern Asia Society for Transportation Studies vol 5 pp2237ndash2249 2005


[40] B Roy ldquoThe outranking approach and the foundations ofELECTREmethodsrdquoTheory and Decision vol 31 no 1 pp 49ndash73 1991

[41] M Bashiri and T H Hejazi ldquoAn extension of multi-responseoptimization in MADM viewrdquo Journal of Applied Sciences vol9 no 9 pp 1695ndash1702 2009

[42] J Lair T Rissanen and A Sarja Life Cycle Management ofConcrete Infrastructures for Improved Sustainability Methods forOptimisation and Decision Making in Lifetime Management ofStructures European Community Competitive and SustainableGrowth Programme 2004

[43] X Damaskos and G Kalfakakou ldquoApplication of ELECTREIII and DEA methods in the BPR of a bank branch networkrdquoYugoslav Journal of Operations Research vol 15 no 2 pp 259ndash276 2005

[44] J R Figueira S Greco B Roy and R Slowinski ELECTREMethods Main Features and Recent Developments vol 298 ofCahier du Lamsadea Laboratoire drsquoAnalyse et Modelisation deSystemes pour lrsquoAide a la Decision 2010

[45] A S Milani A Shanian and C El-Lahham ldquoUsing differentELECTRE methods in strategic planning in the presence ofhuman behavioral resistancerdquo Journal of Applied Mathematicsand Decision Sciences vol 2006 Article ID 10936 19 pages2006

[46] M Rogers and M Bruen ldquoChoosing realistic values of indiffer-ence preference and veto thresholds for usewith environmentalcriteria within ELECTRErdquo European Journal of OperationalResearch vol 107 no 3 pp 542ndash551 1998

[47] J Gong and J Xu ldquoThe integration of valued outrankingrelations in ELECTRE methods for ranking problemrdquo WorldJournal of Modelling and Simulation vol 2 no 1 pp 3ndash14 2006

[48] L F A M Gomes L A D Rangel and R A MoreiraldquoUsing ELECTRE IV in the promotion of social and economicdevelopment a case study in Rio De Janeirordquo Foundations ofComputing and Decision Sciences vol 34 no 3 pp 156ndash1722009

[49] A Shanian and O Savadogo ldquoA non-compensatory compro-mised solution for material selection of bipolar plates for poly-mer electrolyte membrane fuel cell (PEMFC) using ELECTREIVrdquo Electrochimica Acta vol 51 no 25 pp 5307ndash5315 2006

[50] H Y Tsai and T X Bui Implementing a multiple criteria modelbase in Co-op with a graphical user interface generator [MSthesis] Naval Postgraduate School Monterey Calif USA 1993

[51] G H Tzeng T Y Chen and J C Wang ldquoA weight-assessingmethod with habitual domainsrdquo European Journal of Opera-tional Research vol 110 no 2 pp 342ndash367 1998

[52] M Shinohara C Miyake and K Ohsawa ldquoWhy not use theentropy method for weight estimationrdquo in Proceedings of the6th International Symposium on the Analytic Hierarchy Process(ISAHP 01) Berne Switzerland August 2001

[53] FH Lotfi andR Fallahnejad ldquoImprecise shannonrsquos entropy andmulti attribute decision makingrdquo Entropy vol 12 no 1 pp 53ndash62 2010

[54] L Abdullah and A Otheman ldquoA new entropy weight for sub-criteria in interval type-2 fuzzy TOPSIS and its applicationrdquoInternational Journal of Intelligent Systems and Applications vol5 no 2 pp 25ndash33 2013

[55] T Akyene ldquoCell phone evaluation base on entropy and TOP-SISrdquo Interdisciplinary Journal of Research in Business vol 1 no12 pp 9ndash15 2012

[56] Z-H Zou Y Yun and J-N Sun ldquoEntropymethod for determi-nation of weight of evaluating indicators in fuzzy synthetic eval-uation for water quality assessmentrdquo Journal of EnvironmentalSciences vol 18 no 5 pp 1020ndash1023 2006

[57] C E Shannon ldquoAmathematical theory of communicationrdquoTheBell System Technical Journal vol 27 pp 379ndash423 1948

[58] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[59] T L Saaty ldquoHow to make a decision the analytic hierarchyprocessrdquo European Journal of Operational Research vol 48 pp9ndash26 1990

[60] T L Saaty ldquoDecision making with the analytic hierarchyprocessrdquo International Journal of Services Sciences vol 1 no 1pp 83ndash98 2008

[61] Wikimedia Foundation Wikipedia Watt November 2014httpenwikipediaorgwikiWatt

[62] J Eliasson and G Ludvigsson ldquoLoad factor of hydropowerplants and its importance in planning and designrdquo in Proceed-ings of the 11th International Seminar on Hydro Power PlantsHydros Future in Changing Markets University of TechnologyVienna Austria November 2000

[63] ESHA (European Small Hydropower Association) Brochure onEnvironmental Integration of Small Hydropower Plants BrusselsBelgium 2005

[64] M F Scheier and C S Carver ldquoOn the power of positivethinking the benefits of being optimisticrdquo Current Directionsin Psychological Science vol 2 no 1 pp 26ndash30 1993

[65] A K MacLeod and R Moore ldquoPositive thinking revisitedpositive cognitions well-being and mental healthrdquo ClinicalPsychology amp Psychotherapy vol 7 no 1 pp 2ndash10 2000

[66] D E Goodhart ldquoThe effects of positive and negative thinkingon performance in an achievement situationrdquo Journal of Person-ality and Social Psychology vol 51 no 1 pp 117ndash124 1986

[67] D J Siegel The Developing Mind How Relationships and theBrain Interact to Shape Who We Are The Guilford Press NewYork NY USA 2012

[68] TWilliamson ldquoIs knowing a state of mindrdquoMind vol 104 no415 pp 533ndash565 1995

[69] R Likert ldquoA technique for the measurement of attitudesrdquoArchives of Psychology vol 22 no 140 1932

[70] G A Miller ldquoThe magical number seven plus or minustwo some limits on our capacity for processing informationrdquoPsychological Review vol 63 no 2 pp 81ndash97 1956

[71] R M Shiffrin and R M Nosofsky ldquoSeven plus or minus two acommentary on capacity limitationsrdquo Psychological Review vol101 no 2 pp 357ndash361 1994

[72] B Rohrmann ldquoVerbal qualifiers for rating scales sociolin-guistic considerations and psychometric datardquo Project ReportUniversity of Melbourne Melbourne Australia 2007 httpwwwrohrmannresearchnetpdfsrohrmann-vqs-reportpdf

[73] Ermatita S Hartati R Wardoyo and A Harjoko ldquoELECTRE-entropymethod in groupdecision support systemmodelto genemutation detectionrdquo International Journal of Advanced Researchin Artificial Intelligence vol 1 no 1 pp 58ndash63 2012

[74] P le Gauffre R Baur K Laffrechine and M MiramondldquoD7 report survey of multi-criteria techniques and selectionof relevant proceduresrdquo CARE-W EU project under the 5thFramework Program contract no EVK1-CT-2000-00053 2002

[75] J C Leyva-Lopez and E Fernandez-Gonzalez ldquoA new methodfor group decision support based on ELECTRE III methodol-ogyrdquo European Journal of Operational Research vol 148 no 1pp 14ndash27 2003


[76] V Mousseau J Figueira and J-P Naux ldquoUsing assign-ment examples to infer weights for ELECTRE TRI methodsome experimental resultsrdquo European Journal of OperationalResearch vol 130 no 2 pp 263ndash275 2001

[77] V Mousseau and L Dias ldquoValued outranking relations inELECTRE providing manageable disaggregation proceduresrdquoEuropean Journal of Operational Research vol 156 no 2 pp467ndash482 2004

[78] M F Norese ldquoELECTRE III as a support for participatorydecision-making on the localisation of waste-treatment plantsrdquoLand Use Policy vol 23 no 1 pp 76ndash85 2006

[79] P S Nagpaul Guide to Advanced Data Analysis Using IDAMSSoftware 2014 httpwwwunescoorgwebworldidamsadvguideTOChtm

[80] United Nations Educational and Scientific and CulturalOrganization (UNESCO) ldquoCommunication and InformationFree and Open Source Software (FOSS) InternationallyDevelopedDataAnalysis andManagement Software (IDAMS)rdquo2014 httpwwwunescoorgnewencommunication-and-informationaccess-to-knowledgefree-and-open-source-soft-ware-fossidams

[81] G del Bigio ldquoThe UNESCO IDAMS software packages inter-nationally developed data analysis and management softwarerdquoInformation Technology for Development vol 4 no 1 pp 73ndash741989

[82] Wikimedia Foundation Inc Wikipedia IDAMS 2014 httpenwikipediaorgwikiIDAMS

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Table 1 The peak load and the electricity consumption of Turkish Interconnected Electricity System

Year Peak load (MW) Percent change () Electricity consumption (GWh) Percent change ()1996 15231 75 94789 1081997 16926 111 105517 1131998 17799 52 114023 811999 18938 64 118485 392000 19390 24 128276 832001 19612 11 126871 minus112002 21006 71 132553 452003 21729 34 141151 652004 23485 81 150018 632005 25174 72 160806 722006 27594 96 174637 862007 29249 60 190000 882008 30517 43 198085 432009 29870 minus21 194079 minus202010 33392 118 210434 842011 36122 82 229319 90Data and source [14 15]

2530354045505560657075

050

100150200250300350400450500550600650700750800

1961

1963

1965

1967

1969

1971

1973

1975

1977

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2011

Mill

ions

Billi

ons

GDP (current US$)Midyear population

Figure 1 GDP gross domestic product and population in Turkey(generated by the Microsoft Office Excel 2007)Data GDP (currentUSD 1961ndash2012) [12] (left axis) midyear population estimations(1961ndash2012) [13] (right axis)

Region (Azerbaijan Georgia etc) (see and read [9]) theEurope (France Germany etc) (see and read [10]) andthe MENA Region (Middle East and North Africa EgyptMorocco etc) (see and read [11]) This geographical locationalso gives an advantage to Turkey to interconnect its nationalelectricity grid to the other national electricity grids whichalso increases very much the importance of the currentsubject of this experimental research study not only for theperspective of Turkey but also for the perspective of theregions such as the Balkans the Caucasus and the MENA

The Turkish electricity generation establishments can begrouped according to their management styles organizationstructures sizes and business capabilities The diversifiedcharacteristics and properties of these entities in the Turkishelectricity generation market make the business and man-agement models and organizations classification study not

so difficult The decision making process of these entities aredifferent from each other based on these characteristic differ-ences The application and adaptation of several appropriatescientific methods are very important for some entities sothat the more the research studies by the different approachesand methods are conducted in this subject the more theappropriate scientificmethods and approaches will be startedto be used and preferred in the decision making process ofthe private small hydropower plant investments (PSHPPIs)in the practical daily life which will expectedly increase thetotal satisfaction on the PSHPPIs of all of the participants theparties and the involvers

The entities or the investors in the Turkish electricitygeneration sector can either invest in the renewable energysources (RESs) main group or in the fossil fuels sources maingroup The hydropower and the wind power in the RESsmain group and the natural gas and the imported coal in thefossil fuels main group have the major pie or share groups inthis market The projected installed capacity by the primaryenergy resources is presented in Figure 2

The hydropower plants are grouped as one segment with-out considering their installed capacities (each power plant)in this projection Figure 2 shows that the total percentageor share of the installed capacity of the hydropower plantsin Turkey shall be increased or tried to be increased toalmost 40 of the total installed power of the whole powerplants in Turkey until 2020s which indicates and means thatthe subject of this experimental research study will keep itsimportance in the short to long terms and periods Generallythe hydropower plants are classified based on their installedcapacities (119875) as large medium small mini- micro-and picohydropower plants However the consensus on theinstalled capacities of this classification has not been achievedyet For instance the SHPP installed capacity (kW) waspresented as (119875 lt 10000) by Dragu et al [33] (119875 lt 10000)by EREC [34] (1000 lt 119875 le 10000) by ESHA [35]


05

1015202530354045


2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

2021








020406080

100120140160180200220240

2005 2006 2007 2008 2009 2010 2011 2012













Keywords Keywords


and small hydro







lowast 0 1156 448 2 10 0 0TFJ 84 21 1









lowast 0 2

lowast

15

lowast 0 3

lowast 0 2

lowast 0 0TFJ 1

lowast 0 0 1

lowast 0 1

lowast 0 0 0 0WB 1

lowast 0 1




119895and 119901





1 119886

2 119886

119894 119886

119898 where 119898 is


1 119892

2

119892

119895 119892

119899 where 119899 ge 3


119894on the


119895is 119892119895(119886

119894) for all 119886

119894isin 119860 and 119892

119895isin 119865


119902




criterion (V119895

ge 119901

119895ge 119902




119902







hArr

hArr

hArr





ak anak an

ak an

ak an

ak an

or






Otherwise


Figure 5


119895[46]


119895and sum

119895|119892119895isin119865

119908

119895= 1 (1)


119895= 119875

119895cup 119876

119895cup 119868

119895(≻119895= 119876

119895cup 119875

119895)


(≻= 119876 cup 119875)







akSan and anSak






(2)


119888

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus 119902

119895

lt 1

if 119892119895(119886

119899) minus 119901

119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119902

119895

1 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119902

119895

(3)


119862 (119886

119896 119886

119899) =

sum

119899

119895=1119908

119895times 119888

119895(119886

119896 119886

119899)

sum

119899

119895=1119908

119895

(4)

where 119908



119896 119886

119899) is

119889

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus V119895

lt 1

if 119892119895(119886

119899) minus V119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119901

119895

1 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus V119895

(5)



119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)


119904(119886

119896 119886

119899) ge 120582


119904(119886

119896 119886


120582 = 067) then 119886

119896outranks 119886








119898

119901(119886

119896 119886


119896is


119899

119898

119902(119886

119896 119886


119896is


119899

119898

119894(119886

119896 119886


119896is


119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886


which 119886


119899


119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)


119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899


119902 119878

119888 119878

119901 119878V

(8)



119894119895)

119899times119898



119894119895)

119899times119898




119903

119894119895=

119909


119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


(9)




119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










05

1015202530354045


2011

2012

2013

2014

2015

2016

2017

2018

2019

2020

2021








020406080

100120140160180200220240

2005 2006 2007 2008 2009 2010 2011 2012













Keywords Keywords


and small hydro







lowast 0 1156 448 2 10 0 0TFJ 84 21 1









lowast 0 2

lowast

15

lowast 0 3

lowast 0 2

lowast 0 0TFJ 1

lowast 0 0 1

lowast 0 1

lowast 0 0 0 0WB 1

lowast 0 1




119895and 119901





1 119886

2 119886

119894 119886

119898 where 119898 is


1 119892

2

119892

119895 119892

119899 where 119899 ge 3


119894on the


119895is 119892119895(119886

119894) for all 119886

119894isin 119860 and 119892

119895isin 119865


119902




criterion (V119895

ge 119901

119895ge 119902




119902







hArr

hArr

hArr





ak anak an

ak an

ak an

ak an

or






Otherwise


Figure 5


119895[46]


119895and sum

119895|119892119895isin119865

119908

119895= 1 (1)


119895= 119875

119895cup 119876

119895cup 119868

119895(≻119895= 119876

119895cup 119875

119895)


(≻= 119876 cup 119875)







akSan and anSak






(2)


119888

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus 119902

119895

lt 1

if 119892119895(119886

119899) minus 119901

119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119902

119895

1 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119902

119895

(3)


119862 (119886

119896 119886

119899) =

sum

119899

119895=1119908

119895times 119888

119895(119886

119896 119886

119899)

sum

119899

119895=1119908

119895

(4)

where 119908



119896 119886

119899) is

119889

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus V119895

lt 1

if 119892119895(119886

119899) minus V119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119901

119895

1 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus V119895

(5)



119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)


119904(119886

119896 119886

119899) ge 120582


119904(119886

119896 119886


120582 = 067) then 119886

119896outranks 119886








119898

119901(119886

119896 119886


119896is


119899

119898

119902(119886

119896 119886


119896is


119899

119898

119894(119886

119896 119886


119896is


119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886


which 119886


119899


119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)


119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899


119902 119878

119888 119878

119901 119878V

(8)



119894119895)

119899times119898



119894119895)

119899times119898




119903

119894119895=

119909


119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


(9)




119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Keywords Keywords


and small hydro







lowast 0 1156 448 2 10 0 0TFJ 84 21 1









lowast 0 2

lowast

15

lowast 0 3

lowast 0 2

lowast 0 0TFJ 1

lowast 0 0 1

lowast 0 1

lowast 0 0 0 0WB 1

lowast 0 1




119895and 119901





1 119886

2 119886

119894 119886

119898 where 119898 is


1 119892

2

119892

119895 119892

119899 where 119899 ge 3


119894on the


119895is 119892119895(119886

119894) for all 119886

119894isin 119860 and 119892

119895isin 119865


119902




criterion (V119895

ge 119901

119895ge 119902




119902







hArr

hArr

hArr





ak anak an

ak an

ak an

ak an

or






Otherwise


Figure 5


119895[46]


119895and sum

119895|119892119895isin119865

119908

119895= 1 (1)


119895= 119875

119895cup 119876

119895cup 119868

119895(≻119895= 119876

119895cup 119875

119895)


(≻= 119876 cup 119875)







akSan and anSak






(2)


119888

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus 119902

119895

lt 1

if 119892119895(119886

119899) minus 119901

119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119902

119895

1 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119902

119895

(3)


119862 (119886

119896 119886

119899) =

sum

119899

119895=1119908

119895times 119888

119895(119886

119896 119886

119899)

sum

119899

119895=1119908

119895

(4)

where 119908



119896 119886

119899) is

119889

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus V119895

lt 1

if 119892119895(119886

119899) minus V119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119901

119895

1 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus V119895

(5)



119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)


119904(119886

119896 119886

119899) ge 120582


119904(119886

119896 119886


120582 = 067) then 119886

119896outranks 119886








119898

119901(119886

119896 119886


119896is


119899

119898

119902(119886

119896 119886


119896is


119899

119898

119894(119886

119896 119886


119896is


119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886


which 119886


119899


119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)


119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899


119902 119878

119888 119878

119901 119878V

(8)



119894119895)

119899times119898



119894119895)

119899times119898




119903

119894119895=

119909


119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


(9)




119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













lowast 0 2

lowast

15

lowast 0 3

lowast 0 2

lowast 0 0TFJ 1

lowast 0 0 1

lowast 0 1

lowast 0 0 0 0WB 1

lowast 0 1




119895and 119901





1 119886

2 119886

119894 119886

119898 where 119898 is


1 119892

2

119892

119895 119892

119899 where 119899 ge 3


119894on the


119895is 119892119895(119886

119894) for all 119886

119894isin 119860 and 119892

119895isin 119865


119902




criterion (V119895

ge 119901

119895ge 119902




119902







hArr

hArr

hArr





ak anak an

ak an

ak an

ak an

or






Otherwise


Figure 5


119895[46]


119895and sum

119895|119892119895isin119865

119908

119895= 1 (1)


119895= 119875

119895cup 119876

119895cup 119868

119895(≻119895= 119876

119895cup 119875

119895)


(≻= 119876 cup 119875)







akSan and anSak






(2)


119888

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus 119902

119895

lt 1

if 119892119895(119886

119899) minus 119901

119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119902

119895

1 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119902

119895

(3)


119862 (119886

119896 119886

119899) =

sum

119899

119895=1119908

119895times 119888

119895(119886

119896 119886

119899)

sum

119899

119895=1119908

119895

(4)

where 119908



119896 119886

119899) is

119889

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus V119895

lt 1

if 119892119895(119886

119899) minus V119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119901

119895

1 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus V119895

(5)



119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)


119904(119886

119896 119886

119899) ge 120582


119904(119886

119896 119886


120582 = 067) then 119886

119896outranks 119886








119898

119901(119886

119896 119886


119896is


119899

119898

119902(119886

119896 119886


119896is


119899

119898

119894(119886

119896 119886


119896is


119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886


which 119886


119899


119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)


119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899


119902 119878

119888 119878

119901 119878V

(8)



119894119895)

119899times119898



119894119895)

119899times119898




119903

119894119895=

119909


119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


(9)




119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










hArr

hArr

hArr





ak anak an

ak an

ak an

ak an

or






Otherwise


Figure 5


119895[46]


119895and sum

119895|119892119895isin119865

119908

119895= 1 (1)


119895= 119875

119895cup 119876

119895cup 119868

119895(≻119895= 119876

119895cup 119875

119895)


(≻= 119876 cup 119875)







akSan and anSak






(2)


119888

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus 119902

119895

lt 1

if 119892119895(119886

119899) minus 119901

119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119902

119895

1 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119902

119895

(3)


119862 (119886

119896 119886

119899) =

sum

119899

119895=1119908

119895times 119888

119895(119886

119896 119886

119899)

sum

119899

119895=1119908

119895

(4)

where 119908



119896 119886

119899) is

119889

119895(119886

119896 119886

119899)

=

0 if 119892119895(119886

119896) ge 119892

119895(119886

119899) minus 119901

119895

0 lt

119901

119895minus [119892

119895(119886

119899) minus 119892

119895(119886

119896)]

119901

119895minus V119895

lt 1

if 119892119895(119886

119899) minus V119895lt 119892

119895(119886

119896) lt 119892

119895(119886

119899) minus 119901

119895

1 if 119892119895(119886

119896) le 119892

119895(119886

119899) minus V119895

(5)



119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)


119904(119886

119896 119886

119899) ge 120582


119904(119886

119896 119886


120582 = 067) then 119886

119896outranks 119886








119898

119901(119886

119896 119886


119896is


119899

119898

119902(119886

119896 119886


119896is


119899

119898

119894(119886

119896 119886


119896is


119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886


which 119886


119899


119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)


119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899


119902 119878

119888 119878

119901 119878V

(8)



119894119895)

119899times119898



119894119895)

119899times119898




119903

119894119895=

119909


119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


(9)




119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119904(119886

119896 119886

119899) is

119865 (119886

119896 119886

119899) = 119895 isin 119865 | 119889

119895(119886

119896 119886

119899) ge 119862 (119886

119896 119886

119899)

120590

119904(119886

119896 119886

119899)

=

119862(119886

119896 119886

119899) if 119865 (119886

119896 119886

119899) = 0

119862 (119886

119896 119886

119899)prod

119895isin119865

1 minus 119889

119895(119886

119896 119886

119899)

1 minus 119862 (119886

119896 119886

119899)

if 119865 (119886

119896 119886

119899) = 0

(6)


119904(119886

119896 119886

119899) ge 120582


119904(119886

119896 119886


120582 = 067) then 119886

119896outranks 119886








119898

119901(119886

119896 119886


119896is


119899

119898

119902(119886

119896 119886


119896is


119899

119898

119894(119886

119896 119886


119896is


119899

119898

119900(119886

119896 119886

119899) = 119898

119900(119886

119899 119886


which 119886


119899


119899)

119898 = 119898

119901(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119894(119886

119896 119886

119899) + 119898

119900(119886

119896 119886

119899)

+ 119898

119901(119886

119899 119886

119896) + 119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896)

(7)


119878

119902 if119898119901(119886

119899 119886

119896) + 119898

119902(119886

119896 119886

119899) = 0 and119898

119894(119886

119899 119886

119896) le 1 +

119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) + 119898

119901(119886

119896 119886

119899) then 119886

119896119878

119902119886

119899

119878

119888 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119901(119886

119896 119886

119899) and

119898

119902(119886

119899 119886

119896) + 119898

119894(119886

119899 119886

119896) le 1 + 119898

119894(119886

119896 119886

119899) + 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119888119886

119899

119878

119901 if 119898119901(119886

119899 119886

119896) = 0 and 119898

119902(119886

119899 119886

119896) le 119898

119902(119886

119896 119886

119899) +

119898

119901(119886

119896 119886

119899) then 119886

119896119878

119901119886

119899

119878V if 119898119901(119886119899 119886119896) = 0 and 119886

119896119878

119901119886

119899or 119898

119902(119886

119899 119886

119896) = 1

and no 119886

119899119875119881

119895119886

119896forall119895 and 119898

119901(119886

119896 119886

119899) ge (1198982) in which

119886

119899119875119881

119895119886

119896 (119892119895(119886

119899) lt 119892

119895(119886

119896) + V119895(119892

119895(119886

119896)) then 119886

119896119878V119886119899


119904(119886

119896 119886

119899) is

120590

119904(119886

119896 119886

119899) =

1 if 119886119896119878

119902119886

119899

08 if 119886119896119878

119888119886

119899

06 if 119886119896119878

119901119886

119899

035 if 119886119896119878V119886119899


119902 119878

119888 119878

119901 119878V

(8)



119894119895)

119899times119898



119894119895)

119899times119898




119903

119894119895=

119909


119894119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


119903

119894119895=

max119894119909

119894119895 minus 119909

119894119895

max119894119909

119894119895 minusmin

119894119909

119894119895


(9)




119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119890

119894= minus119896

119898

sum

119895=1

119891

119894119895ln (119891

119894119895)

where 119891

119894119895=

119903

119894119895

sum

119898

119895=1119903

119894119895

119896 =

1

ln (119898)

when 119891

119894119895= 0 997904rArr 119891

119894119895ln (119891

119894119895) = 0


119894=

1 minus 119890

119894

119899 minus sum

119899

119894=1119890

119894

where 0 le 119908

119894le 1

119899

sum

119894=1

119908

119894= 1

(10)







119875 = 120578tr times 120578

119892times 120578

119905times 120588













Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Objectivecriteria










information form



Subjectivecriteria




















Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Action Cr01(km2)

Cr02(hm3)

Cr03(m)

Cr04(m3s)

Cr05(GWh)

Cr06(GWh)



A2 61 48 388 3 6 31 78 uPVC pipe 3300m










1and EDM




120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










120582 = 067

120582 = 085

120582 = 090

Smal

l hyd

ropo

wer

pla

nts i

nves

tmen

t sele

ctio

n in

pre

-dev

elopm

ent i

nves

tmen

t sta

ge

Goal

Subjectivecriteria



Net headFlow rate


cost

River basin

Community attitude



Geology


Securityconditions

Protectedareas



Action 1

Action 2

Action 3

Methods

Cut level

Cut level

Cut level

Results

Action 4

Action 5




alternatives

Note For all

methods





ELECTRE IV



Mai

n ex

perim

enta

lBa

ckbo

ne ex

perim

enta

lM

ain

expe

rimen

tal

Mai

n ex

perim

enta

l

Comparision of

discrimination

Comparision of



NoteAnalyze

experimentalresults



(quantitative)

Decision


Objective criteria

IIISE1

IIISE2

IIISE3

IIISA1

IIISA2

IIISA3

IIIEW1

IIIEW2

IIIEW3

IV1IV2

IV3

1

2

3

4

5

A1A2 A3 A4 A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2

IV3

makersrsquo

makersrsquo

120582 Cut level





1) and 01155 (EDM

2)

00780 (EDM1) and 00782 (EDM

2) 00509 (EDM

1) and

00498 (EDM2) 00639 (EDM

1) and 00658 (EDM

2) minus01419


2) minus01111 (EDM

1) and minus01235


1) minus00864 (EDM

2) respectively



2took




000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000 004 008 012 016 020


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003


Net headFlow rate





GeologySecurity


Substation

000

003

006

009

012

015

minus015

minus012

minus009

minus006

minus003

EDM1 EDM2

EDM1 EDM2

EDM1 EDM2





Net headFlow rate





GeologySecurity


Substation











119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















119896 119886

119899) =

sum

119910119910

119911=1119908

119911times 119888

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(12)


1 119911

2 119911

119894 119911

119910119910

Consider


sum

119910119910

119911=1119908

119911times 119908

119895119911

sum

119910119910

119911=1119908

119911


119896 119886

119899)=

sum

119910119910

119911=1119908

119911times119889

119895119911(119886

119896 119886

119899)

sum

119910119910

119911=1119908

119911

(13)



085) and (120582 = 090)





0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

00000020004000600080010001200140016001800200

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17

0100200300400500600700800900

10001100

Cr01

Cr02

Cr03

Cr04

Cr05

Cr06

Cr07

Cr08

Cr09

Cr10

Cr11

Cr12

Cr13

Cr14

Cr15

Cr16

Cr17



EDM1qjEDM2qj

EDM1pjEDM2pj

EDM1vjEDM2vj

EDM1wjEDM2wj





Alte

rnat

ives

(act

ions


1 0 1 1 1 4 A5 4 1 3 1 1 1W 5 4 3 5 1



A1

A1A1

A1 A1 A1A2

A2

A2

A2

A2

A2A2

A3 A3

A3

A3

A3

A4

A4

A4

A4 A4

A4A5

A5 A5 A5

A5

A5

A1A2

A3

A4A3

01234

0 1 2 3 4

A5A3

Asc

endi

ng

Descending

A2

A1 A4minus2

minus2




Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Criterion EDM1

EDM2

Indifference 119902


119895Veto V



119895Veto V

119895





A1 A2 A3 A4 A5A1 1000 0953 0829 0904 0000A2 0871 1000 0870 0953 0000A3 0858 0978 1000 0938 0000A4 0893 0878 0839 1000 0000A5 0916 0848 0903 1000 1000


A1 A2 A3 A4 A5A1 1000 0976 0931 0966 0000A2 0892 1000 0976 0990 0000A3 0594 0986 1000 0904 0000A4 0929 0915 0967 1000 0000A5 0920 0887 0965 1000 1000


A1 A2 A3 A4 A5A1 1000 0941 0864 0918 0000A2 0823 1000 0923 0978 0000A3 0808 0981 1000 0918 0000A4 0879 0866 0894 1000 0000A5 0917 0837 0929 1000 1000

ELECTRE IV

A1 A2 A3 A4 A5A1 1000 0000 0000 0000 0000A2 0000 1000 0000 0000 0000A3 0000 0000 1000 0800 0000A4 0000 0000 0800 1000 0000A5 0000 0000 0000 0000 1000

















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















Alte

rnat

ives

(act

ions


13 3 3


1 0 1 1 1 4 A5 4 1 3 1 1 1W 2 3 2 5 1A5

A1A2

A4A3

01234

0 1 2 3 4

A5

A4

Asc

endi

ng

Descending

A2A1 A3minus1

minus4



A1

A2

A3A4

A5A5

A1

A2

A3A4

A1

A3

A2

A4

A2 A4

A1

A2

A3A4

A5A4

A1

A2

A3

A5A2

A1

A3

A5A1

A3A5








IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IIIE

W3

IV1

IV2

IV3

1

2

3

4

5

A1A2A3A4A5

54

3

2


IIISE2IIISE3

IIISA1IIISA2

IIISA3IIIEW1

IIIEW2IIIEW3

IV1IV2IV3



AA2A3A4

IIIS

E1II

ISE2

IIIS

E3II

ISA

1II

ISA

2II

ISA

3II

IEW

1II

IEW

2

IEW

3

IV1

2





119895) the


119895) was








Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgment


References




























































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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