Page - 188 - in Emerging Technologies for Electric and Hybrid Vehicles

Energies 2016,9, 270 Shannonentropy is capableofevaluating thedecisionmakingunitsandbeingemployedasa weightingdecisionmethod. AssumethataMCDMproblemcontainsmalternativesandn criteria, thus thedecisionmakingmatrix isdefinedasbelow:»————– x11 x12 ¨¨¨ x1n x21 x22 ¨¨¨ x2n ... ... ... ... xm1 xm2 ¨¨¨ xmn fiffiffiffiffifl (22) Then, the criteria weights can be determined based on the entropy concept through the followingsteps: Step1:Normalize theevaluationcriteriaasbelow: Pij “ xijř j xij (23) Specially, for the fuzzyMCDMproblem, the fuzzydecisionmakingmatrixshouldbedefuzzyed firstly,accordingtoEquation(21). Step2:Calculate theentropymeasureofeachcriterionas [51]: ej “´k nÿ j“1 PijlnpPijq (24) wherek=(ln(m))–1. Step3:Definethedivergenceofeachcriterionthrough: divj “1´ej (25) Themore thedivj is, themore important the jthcriterion is. Step4:Determinedthenormalizedweightsofall criteria through[54]: wj “ divjř j divj (26) Finally, the combination weights of all criteria are equal to the average of subjective and objectiveweights. 4.TheFrameworkof theIntegratedMCDMModel TheproposedframeworkforoptimalsitingofelectricvehiclestationbasedonFDM,combination weightingandfuzzyGRA-VIKORmethods involves the followingthreephases (Figure1). 188