Page - 184 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 Step 1: Administer questionnaires anddetermine themost conservative value and themost optimisticvaluerangingfrom0to10foreachcriterionamongagroupofexperts. Step2:Gather theminimumandmaximumvaluesandcalculate thegeometricmeanforeach criterion. Then, compute theconservativeTFN(Ci L ,Ci M ,Ci U ) andoptimisticTFN(Oi L ,Oi M ,Oi U ) in terms of each criterion. Ci L andOi L represent theminimumremaining conservativevalueandminimum remainingoptimisticvalue, respectively;Ci U andOi U represent themaximumremainingconservative valueandmaximumremainingoptimisticvalue, respectively;andCi M andOi M represent thegeometric mean of the remaining conservative value and the geometric mean of the remaining optimistic value, respectively. Step3:Check that theconsistencyofexpertopinions,andcompute theconsensussignificanceGi foreachcriterion. (1) IfCiU ď OiL, the criterion iholds consensus, and thevalueof the consensus significanceGi is computedbyEquation(7): Gi “ G i M`OiM 2 (7) (2) IfCiU ą OiL, and the gray zone interval value (Zi “ CiU ´OiL) is smaller than the interval valueMi “OiU´CiM, correspondingly, thevalueof theconsensussignificance iscomputedby Equation(2): Gi “ “pCiUˆOiMq´pOiLˆCiMq‰““pCiU´CiMq`pOiM´OiLq‰‰ (8) WhenCiU ąOiL, however, thegrayzone intervalvalue (Zi “ CiU´OiL) is greater than the interval value (Mi “OiU´CiM),whichmeans that theexpertopinionsare inconsistent. Thus,Steps1–3should berepeateduntileachcriterionconvergesandthevalueof theconsensussignificancecanbecalculated. 3.3. FuzzyGRA-VIKORMethod TheVlsekriterijumskaOptimizacijia IKompromisnoResenje (VIKOR)method,put forwardby Opricovic in 1998,wasdeveloped formulti-criteria optimizationof complex systems. Thismodel focusesonrankingdifferentalternativesagainstvariousevenconflictingdecisioncriteria. It relieson anaggregating function that canreflectdistance tobothpositiveandnegative idealpoints [47]. In order tohandle the imprecisionandsubjectivityofdecisionmakers, linguisticvaluesare introduced into theconventionalVIKOR.ThefuzzyVIKORcombines theadvantagesof theconventionalVIKOR andfuzzyset theory,which ismuchmoresufficient tomodelproblems in therealworld thanprecise values [12–14,48,49]. In fuzzyVIKOR, themulti-criteriameasurementprocess forrankingalternatives isdeveloped fromanaggregatingfunction,whichrepresents thedistanceofeachalternative frompositive ideal pointandnegative idealpoint.Asmentioned in the introduction, inorder tobetterexamine theextent of theconnectionbetweenalternativeandidealpoints,greyrelationanalysis isusedtomodify the conventionalaggregatingfunction,whichcanbetter identifyrelationshipsamongfuzzynumbers in a system[15,16]. Moreover, the fuzzyVIKORbasedonGRAmethodcanefficientlyovercome the deficienciesof fuzzyresultsandthe inconsistent rankingofalternatives [17,18].Moredetailsof this approachareshownasbelow: Here, theratingsofcriteriaareexpressedin linguistic terms(the triangular fuzzynumbers),as inTable1. 184