多准则决策分析方法

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1、多準則決策分析方法馮正民教授交通大學交通運輸研究所逢甲大學交通工程與管理學系95.6.19WhyweneedMCDM?Theconventionalsingle-criteriondecisionmethodssuchascost-benefitanalysiscanonlydealwiththemonetaryterms.Thedecisionmakerfacesmultipleconflictingobjectivesratherthansingleobjective.Theconflictnatureofaprobleminvolvesseveralinterestgrou

2、psinsteadofasinglegroup.Manyintangibleandincommensurableeffectsinconventionaldecisionmakingmethodscouldnotbeincluded.2多準則決策分析方法／馮正民WhatisMCDM?MCDMisasetofmethodstohelpthedecisionmakerstodescribe,evaluate,rankandselectalternativesaccordingtoseveralcriteria.Twomainclassesofmethodsare:MOP(multio

3、bjectiveprogramming)MCE(multicriteriaevaluation)3多準則決策分析方法／馮正民WhatarethecomponentsinMOP?asetofobjectivefunctions={}asetofdecisionvariables={}asetofconstraints={}TheMOPproblemcanbedefinedmathematicallyasfollows:Subjectto4多準則決策分析方法／馮正民WhatarethecomponentsinMCE?5多準則決策分析方法／馮正民TypesofMCE6多準則決策分析方法

4、／馮正民WeightingofCriteria–AHP建立層級關係建立成對比較矩陣求解權重並檢定一致性7多準則決策分析方法／馮正民AHP(分析階層程序法)8多準則決策分析方法／馮正民WeightingofCriteria–AHPDevelopingImportanceComparisonA=9多準則決策分析方法／馮正民WeightingofCriteria–AHPCheckingtheConsistencyofJudgementsDefinetheconsistencyindex(CI)as:Wherenisthenumberofcriteriaincomparison.10多準

5、則決策分析方法／馮正民WeightingofCriteria–AHPCheckingtheConsistencyofJudgementsDeterminetheconsistencyratio(CR)bydividingCIbyarandomindex(RI):WhereRIisfoundasfollows:Sincewehaven=3,andthusRI=0.58,CRcanbecomputedas:11多準則決策分析方法／馮正民ComputingtheScoresofAlternatives—SAWSAWThroughSAW,wecangetthescoresofthreea

6、lternatives:Since>>,wethereforeselect.12多準則決策分析方法／馮正民ComputingtheScoresofAlternatives—TOPSIS13多準則決策分析方法／馮正民ComputingtheScoresofAlternatives-TOPSIS將準則評估正規化將正規化之評估值乘上準則權重決定理想解與負理想解計算各方案在各準則表現距理想解以及距負理想解之距離計算對理想解之相對接近程度決定方案優劣順序14多準則決策分析方法／馮正民TOPSIS案例TOPSIS法準則評估值正規化說明[註]：Ci代表準則i，Aj代表方案j。15多準則決策分析

7、方法／馮正民TOPSIS法評估值加權說明例TOPSIS案例理想解={0.5,0,0.3}負理想解={0,0.2,0}16多準則決策分析方法／馮正民TOPSIS距離計算說明例TOPSIS案例如17多準則決策分析方法／馮正民TOPSIS之Cj*值計算例TOPSIS案例18多準則決策分析方法／馮正民質化與量化多準則評估法19多準則決策分析方法／馮正民發展趨勢「不確定性(uncertainty)」的處理「多決策者(multipledecisionmakers)」的處理方法之間的比較與評估