基于关联的多属性决策分析理论及其应用研究

南京航空航天大学博士学位论文基于关联的多属性决策分析理论及其应用研究姓名：章玲申请学位级别：博士专业：管理科学与工程指导教师：周德群20070401I1TOPSISTOPSISTOPSIS2λλR-R-R-R-3TOPSISELECTRESugenoR-4///II5IIIABSTRACTMulti-attributedecisionmaking(MADM)hasalwaysbeenahotspotinresearchareasduetoitswideapplicationinpracticefieldsofengineering,economicsandmanagement,wheremanyproblemscanbemodeledbyMADM.However,applicationachievementsinMADMarenotasabundantastheoreticalachievementsinthisarea.InordertostrengthenthecombinationoftheoryandapplicationofMADM,MADMwithinteractionhasrecentlyturnedouttobeaforwardpositiontechnologyindecision-makingfield.TherearestillmanyproblemsintheareaofMADMwithinteractionneededtobestudiedandsolvedinthefuture,suchasthedefinitionofthecorrelationofalternatives,theMADMproblemswithvariableweightswhenthecriteriaareinteraction,andthehierarchicalMADMproblemsunderthepoor-informationsituationwhentheattributesareinteraction.Therefore,thepurposeofthispaperistodoadeepresearchonallofthesethreequestions.Thedetailedarrangementofthispaperstandsoutasfollows:(1)StudyontheinteractionamongalternativesinMADM.Firstofall,theinteractionamongalternativesisdefined,andthencorrelationamongthealternatives’interaction,independenceofirrelevantalternativesandreversalrankingareanalyzed.Second,throughcasestudyandtheorydeduction,alternatives’interactioninlinearallocationmethod,weightedaveragemethodandTOPSISmethodarestudied,basedonwhichtworankingpreservationmethodsforWA(WeightedAverage)areproposed.Finallywecandrawtheconclusionthatalternatives’interactioncanalsobeintroducedintoabsoluteTOPSISwhilethedecision-makingresultsfromthepairwisecomparisonofTOPSISmaynotsatisfytheruleoftransitivity.(2)StudyontheMADMtheorywithattributes’interaction.Consideringthewideapplicationofλfuzzymeasureindecision-makingproblem,λfuzzymeasureanditstwotransformingforms-MÖbiustransformationandinteractioncoefficients-arededucedbasedontheexistingreferences.Takingtheshortcomingoftheconstantweightsintoconsideration,thedefinitionsandpropertiesofthevariableweightswithinteraction(R-variableweights)andlocalstatevariableweightvectorwithinteraction(R-localstatevariableweight)areanalyzedbasedonfuzzymeasuretheoryandtraditionalvariable-weighttheory.TheresearchresultsdemonstratethefactthattheR-variableweight(orR-localstatevariableweight)isthegeneralformofthevariableweight(orlocalstatevariableweight).IV(3)StudyontheMADMmethodwithattributes’interaction.Thenewmethodscalledlinearallocationmethodwithinteraction,weightedaveragemethodwithinteraction,TOPSISmethodwithinteraction,ELECTREmethodwithinteractionandorderedSugenomethodareproposedinthelightoffuzzymeasuresandintegrals.Thenthepropertiesandapplicationstepsofthesemethodsarealsodiscussed,andtheirvalidityistestedwithexamples.Afterthat,MADMmethodwithvariableweightswhenattributesareinteractionisdiscussedbasedontheR-variableweightstheory.Finally,correspondingmodelisestablishedtocomputetheweightsofattributesandtheircoalitions,andoneexampleisusedtoillustratethevalidityofthemodelaswellasthemethod.(4)StudyonthehierarchicalMADMmethodwithattributes’interaction.Firstly,anewmethodtodividehierarchicalstructuresforcomplexsystemsisputforwardbasedontheintegrationofDEMATELandISM,andthenthehierarchicalMADMmodelisanalyzed.Sinceitisoftendifficultfordecisionmakersandexpertstoprovideenoughpreferenceinformationforreferenceattributesandalternatives,underthepoor-informationsituationthemethodofsolvingthehierarchicalMADMproblemwithconstantweightsandvariableweightsareanalyzedrespectivelywhenattributesareinteractive.ThefactthatthehierarchicalMADMmethodwithconstantweightsandvariableweightswhenattributesareinteractionarethegeneralformofhierarchicalMADMmethodwithconstantweightsandvariableweightswhenattributesareindependentisconcluded.(5)StudyonapplicationoftheMADMtheorywithattributes’interactiontotrans-regionalinvestmentofcoalenterprise.Firstly,settinginthebackgroundoftrans-regionalinvestmentofcoalenterprise,itstudiesdeterminantsofperiodchoice,andwithvariable-weightsMADMmethodwithinteraction,theperiodchoiceforthetrans-regionalinvestmentofcoalenterpriseisdiscussed.Thenthedeterminantsoflocationchoiceareresearched,basedonwhich,thelocationchoiceforthetrans-regionalinvestmentofcoalenterpriseissolvedbyhierarchicalMADMtheorywithinteraction.Keywords:Multi-attributedecisionmaking,Interaction,Idependencefromirrelevantalternatives,Rankreversals,Fuzzymeasure,Variableweight,CoalenterpriseVIII1.1MCDMMADMMADM..........................................21.2MADM...............................................................41.3........................................................................................122.1LAM...............................................................152.2....................................................................................................172.3.................................................................................................172.4WAA.......................................................202.5TOPSIS...............................................263.1n=4[85]...........................