一种基于差异度变权的多属性决策方法

135Vol．13No．5201210JOURNALOFBEIHUAUNIVERSITYNaturalScienceOct．20121009-4822201205-0506-05050003、．．．O159A2012-04-241980－．AMulti-attributeDecisionMethodBasedonDeviationDegreeVariableWeightsWANGZhi-liLIDe-qingMENGMing-qiangBasicCoursesofOrdnanceEngineeringCollegeShijiazhuang050003ChinaAbstractThemulti-attributedecisionwhichinformationonattributeweightsisunknowncompletelywedefinethedeviationdegreeoftheattributevalues．Andthenweproposeamulti-attributedicisionmethodbasedonit．Theproposedmethodcandeterminetheweightsofattributesobjectively．Basedondeviationdegreeweutilitythestateweightsvectorrealizethebalanceoftheattributevalues．Finallyanexampleisgiventoillustratethefeasibilityandeffectivenessofthemethod．Keywordsdeviationdegreevariableweightsstatevariableweightsmulti-attributedecision01-2．、、、．3．．、、0．80．90．70．80．70．8．1/3．4．．、．．．．“”．11．156-7．14nnWjj=12…nWj01n→01x1x2…xm→Wjx1x2…xnw1∑nj=1Wjx1x2…xn=1w2Wjx1…xnj=12…nw3Wjx1…xnj=12…nxj．X=x1x2…xnWX=W1X…WnX．w3．w3w3'Wjx1…xnj=12…nxj．WX=W1X…WnX．24S01m→01mXSX=S1XS2X…SnXns1xi≥xjSiX≤SjXs2SjXj=12…ns3W=w1w2…wnWX=W·SX∑mk=1wkSkX11w1w2w31．W·SX=w1S1Xw2S2X…wnSnXHadamard．s1．SX．1．2A=A1A2…AmU=u1u2…unW=w1w2…wnwj≥0∑nj=1wj=1H．H．xijAiujxi=xi1xi2…xini=12…mAiA=xijm×n．．ijrij=fjxiji=12…mj=12…n．f、．rij∈01rijAiuj．R=rijm×n．Ai8MiX=∑nj=1wjrijj=12…n．2270552．1．2．2．ujuj．．．ujuj．．3drijrik=rij－rikR=rijm×nrijrik．ujAiDijAiDijAi=∑mk=1drijrkj．αj=∑mi=1DijAi=∑mi=1∑mk=1drijrkjj=12…nujαj．4nnWjj=12…nWj01n→01α1α2…αnWjα1α2…αnw1∑nj=1Wjα1α2…αn=1w2Wjα1α2…αnj=12…nαjw3Wjα1α2…αnj=12…nαj．W=W1αW2α…Wnα．αj=0ujujwj=0．1f瓗n→瓗nα1α2…αnfα1α2…αnfα1α2…αnαj≥0wjα=fjα∑nk=1fkαuj．4．．α=α1α2…αnfjα=eαj－1wjα=eαj－1∑nk=1eαk－1uj．αj=0wj=0．uj．．2．21．R=r11r12…r1nr21r22…r2nrm1rm2…rmnm×n80513W=w1w2…wnwj≥0∑nk=1wj=1．2．ujαjαj=∑mi=1Dijxi=∑mi=1∑mk=1drijrkj．αjwjα2．3．W=w1αw2α…wnα1Mii=12…m．Mi．4“”．．．8-9．7WXSjXWX=W·SX∑nj=1wjSjX．58．2W=w1w2…wnMi=∑nj=1wjXrijj=12…nri=ri1ri2…rini=12…mAi．．11．．3．u1、u2、u3、u4．、、、R=rij=0．75140．60650．80000．88240．70000．88240．80000．75140．88241．00000．80000．60650．70650．75140．80001．0000．1W=0．250．250．250．25．Mi=∑4j=1wjrij0．76010．78340．82220．8145．．2．ujαj1α1=1．1842α2=2．6230α3=0α4=2．6230．u2u4u3．wjα1α2α3α4=eαj－1∑4j=1eαk－1．90550．080．4600．46Wα1α2α3α4=0．080．4600．46．0．74500．80750．80960．8622．．1．α3=0u3“1”．．u2u4u1u3u2u4“1”u1．u2u40．46．．．．“”．．．32Wα1α2α3α4=0．080．4600．46Sjri=eαriji=1234j=1234．α=－20．71080．79770．73940．8307．2．、0．6065．μ21．0000μ4．、．．3u40．460．3380．5100．6430．338．u1．4．．．．．1BlackmanSS．Multiple-targetTrackingwithRadarApplicationsM．DedhamArtechHouse1986．2DLHall．MathematicalTechniquesinMulti-sensorDataFusionM．NorwoodArtechHouse1992．3HwangCLandYoonK．MultipleAttributeDecisionMakingMethodsandApplicationsM．NewYorkSpring-Verlag1981．4．Ⅷ———J．1995931-9．5．M．1985．6．Ⅸ———Weber-FechneJ．199610212-19．7．Ⅹ———J．199610410-18．8．J．200415109-119．9．J．200419111241-1245．10．J．20031212104-109．11．VagueJ．20045103-109．【】01513