Page - 187 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 A(1),A(2),A(3), . . . A(M), if the condition (II) is not satisfied;A(M) is determinedby the relation Q(A(M) –A(1))<DQ, formaximumM (thepositionsof thesealternativesare“incloseness”). 3.4. TheCombinationWeights Theweighted sumof the “distances” fromanalternative to corresponding ideal points over all criteria is essential for performance comparison among all designated alternatives. From the previous literatureonMCDM,theweightsofcriteriaareusuallysubjectiveweightsdeterminedby decisionmakers. However, critiquesofhumanerrors and inconsistencyareoftenassociatedwith subjectiveweights forsuchweightingprocesses inMCDM.Withthis regard, to improvetheweighting accuracy, someobjectiveweightingmodelsareappliedbymathematical techniques. Toobtainabetter weightdeterminingsystemfor fuzzyVIKOR,combinationweightsbasedonsubjectivemethodsand objectivemethodsare introducedinthisstudy,whichcancompositesubjective judgmentandobjective information. Ontheonehand, thesubjectiveweightsaredeterminedbyexperts’opinions. Onthe otherhand, theobjectiveweightsareobtainedbytheShannonentropymethod. 3.4.1. TheSubjectiveWeights On theonehand, the subjectiveweights couldbeobtained fromexperts’ opinions. Here, the ratingsofcriteriaareexpressed in linguistic terms(the triangular fuzzynumbers), as inTable2. Table2.Fuzzyevaluationscores forcriteriaweights. LinguisticTerms MembershipFunction Oflittle importance (0,0,0.3) Moderately important (0,0.3,0.5) Important (0.2,0.5,0.8) Very important (0.5,0.7,1) Absolutely important (0.7,1,1) Letrsjk “ ´sLjk,sMjk ,sUjk¯, 0 ď sLjk ď sMjk ď sUjk ď 1,j “ 1,2, ¨¨¨n,k “ 1,2, ¨¨¨r be the superiority linguistic ratingoncriteriaweightassignedtocriteriaCjbyexpertDk canbecalculatedby: rsjk “´sLjk,sMjk ,sUjk¯“ ˜ rÿ k“1 sL jk r , rÿ k“1 sM jk r , rÿ k“1 sU jk r ¸ (20) Inordertomaintaintheconsistencybetweenobjectiveweightsandsubjectiveweights, thecriteria weightsbasedontriangular fuzzynumbersshouldbealsodefuzziedbasedonEquation(21). In this paper, thegradedmean integrationapproach isemployed to transformatriangular fuzzynumber M=(l,m,u) intoaprecisenumber: P ´ĂM¯“M“ l`4m`u 6 (21) 3.4.2. ShannonEntropyandObjectiveWeights TheentropyconceptproposedbyShannon in1948 is ameasureofuncertainty in formulated information,whichhasbeenwidelyusedinmanyfieldssuchasmanagement, engineeringandsoon. Accordingto the idealofentropytheory, thenumberorqualityof informationfromdecision-making process isdeterminedbytheaccuracyandreliabilityof thedecision-makingproblem[52]. Therefore, entropycanbeappliedto theassessmentproblemindifferentdecision-makingprocesses.Moreover, entropycanalsobeusedtoanalyzethequantityof informationprovidedbydata[53]. Thebasic theory andspecificstepsofShannonentropyweightingmethodareshownasbelow: 187