对方案有偏好的直觉模糊多属性决策方法

2009，45（2）1Zadeh1965[1]Atanassov[2]BustinceBurillo[3]GauBuehrer[4]Vague。、。。ChenTan[5]1994Vague。HongChoi[6][5]Vague。[7-9][5-6]。[10]TOPSIS。。D.F.Li[11]2005。[12-13][11]。。。21[2]XA={xμAxνAx|x∈X}μAxνAxXxAμAX→[01]νAX→[01]0≤μAx+νAx≤1x∈X。1-μAx-νAx。XxAμAxνAx。XAA={μAxνAx|x∈X}。XIAMei-meiWEICui-ping276826CollegeofOperationsResearchandMana[e-mail]zymultipleattributedecisionmakingwithpreferencerelationonalternatives.ComputerEngineeringandApplications2009452137-139.AbstractAmethodispresentedtodealwiththefuzzymultipleattributedecisionmakingproblemwithpreferencevaluesonal－ternativesinwhichtheinformationaboutattributeweightsisincompletetheattributevaluesandthepreferenceinformationonalternativesaregivenintheformofintuitionisticfuzzynumbers.Accordingtothepreferenceinformationonalternativesgivenbydecisionmakersmulti-objectiveprogrammingmodelisconstructedtoobtaintheattributeweights.Thenintuitionisticfuzzyweightedarithmeticaveragingoperatorisusedtoaggregatetheintuitionisticfuzzyinformationcorrespondingtoeachalternativeandtheal－ternativesarerankedbythescorefunction.Finallyanillustrativeexampleisgiventodemonstratethepracticalityandeffective－nessoftheproposedmethod.Keywordsmultipleattributedecisionmakingintuitionisticfuzzynumbersobjectiveprogrammingmodelweightedarithmeticav－eragingoperator、。。DOI10.3778/j.issn.1002-8331.2009.02.0401002－8331200902-0137-03AC934theNationalNaturalScienceFoundationofChinaunderGrantNo.10671108theNaturalScienceFoundationofShandongProvinceofChinaunderGrantNo.Y2005A04。1984－1972－、。2008-08-182008-10-23ComputerEngineeringandApplications137ComputerEngineeringandApplications2009，45（2）aba∈[01]b∈[01]a+b≤1。Ω。坌αj=ajbj∈Ωj=12。[14]1α1茌α2=a1+a2-a1a2b1b22α1茚α2=a1a2b1+b2-b1b23λα1=1-1-a1λbλ1λ04αλ1=aλ11-1-b1λλ0。2[14]坌α=ab∈Ωsα=a-b2αHα=a-b2α。坌αj=ajbj∈Ωj=12。[14]1Sα1Sα2α1α22Sα1=Sα2Hα1Hα2α1α2Hα1=Hα2α1=α2Hα1Hα2α1α2。3[14]αj=ajbjj=12…nfΩn→Ω。fwα1α2…αn=w1α1茌w2α2茌…茌wnαn=1-nj=1仪1-ajwjnj=1仪bwjjjjΩw=w1w2…wnTαjj=12…nwj∈[01]nj=1Σwj=1f。w=1n1n…1nnnTf。3A={A1A2…Am}C={C1C2…Cn}AiCjαijaijbijaijbijAiCj0≤aijbij≤10≤aij+bij≤1i=1…mj=1…n。R=αijm×n。AiαiaibiaibiAi0≤aibi≤10≤ai+bi≤1i=1…m。。w=w1w2…wnT3Aizizi=fwai1bi1ai2bi2…ainbin=1-nj=1仪1-aijwjnj=1仪bwjijjni=1…m1ziAi。1。[15]1{wTAw≥bw0b≥0}2{wTAw≤bw0b≥0}3{wTAw=bw0b≥0}。Al×n。H。Mindi1=1-nj=1仪1-aijwj-aii=12…m2Mindi2=nj=1仪bwjij-bii=12…m3Mindi3=1-1-nj=1仪1-aijwjjn-nj=1仪bwjij-1-ai-bii=12…m4s.t.w∈Hmj=1Σwj=1wj≥0j=12…n52~5Mind=mi=1Σκi1d-i1+λi1d+i1+κi2d-i2+λi2d+i2+κi3d-i3+λi3d+i36s.t.1-nj=1仪1-aijwj-ai-d+i1+d-i1=0i=1…m7nj=1仪bwjij-bi-d+i2+d-i2=0i=1…m81-1-nj=1仪1-aijwjjn-nj=1仪bwjij-1-ai-bi-d+i3+d-i3=09w∈Hmj=1Σwj=1wj≥0j=12…n10d+ikd-ik=0d+ik≥0d-ik≥0i=12…mk=123116~11d-ikdik0d+ikdik0κikλikd-ikd+ik。κik=λik=1i=12…mk=123。16~11w*=w*1w*2…w*nT。21Aizii=12…m。32ziSziHzi[15]ziAii=12…m。41。A1A2A3。A={A1A2A3}。C1C2C3C={C1C2C3}。w=w1w2w3T1382009，45（2）H={0.25≤w1≤0.40.35≤w1≤0.60.3≤w1≤0.35w1≤w3}AiCjaijbij。Aii=123aibiα1=0.250.25α2=0.350.4α3=0.30.65。16~11Mind=3i=1Σd-i1+d+i1+d-i2+d+i2+d-i3+d+i3s.t.1-0.25w1×0.2w2×0.6w3-0.25+d+11-d-11=00.1w1×0.15w2×0.45w3-0.25+d+12-d-12=01-0.25w1×0.2w2×0.6w3-0.1w1×0.15w2×0.45w3-0.5+d+13-d-13=01-0.4w1×0.32w2×0.25w3-0.35+d+21-d-21=00.25w1×0.2w2×0.05w3-0.4+d+22-d-22=01-0.4w1×0.32w2×0.25w3-0.25w1×0.2w2×0.05w3-0.25+d+23-d-23=01-0.2w1×0.55w2×0.4w3-0.3+d+31-d-31=00.2w1×0.5w2×0.3w3-0.65+d+32-d-32=01-0.2w1×0.55w2×0.4w3-0.2w1×0.5w2×0.3w3-0.05+d+33-d-33=00.25≤w1≤0.40.35≤w1≤0.60.3≤w1≤0.35w1≤w3w1w2w3≥0w1+w2+w3=1d+ikd-ik=0d+ik≥0d-ik≥0i=12…mk=123MATLABw*=0.30.40.3d+11=0d-11=0.4527d+12=0.0653d-12=0d+13=0d-13=0.018d+21=0d-21=0.3323d+22=0.2589d-22=0d+23=0d-23=0.2912d+31=0d-31=0.331d+32=0.3241d-32=0d+33=0d-33=0.2551。21zii=123。z1=0.70270.1847z2=0.68230.1411z3=0.63100.3259。32zii=123。Sz1=0.5180Sz2=0.5412Sz3=0.3051[15]ziA2酆A1酆A3A2。5。。[1]ZadehLA.Fuzzysets[J].InformationandControl19658338-356.[2]AtanassovK.Intuitionisticfuzzysets[J].FuzzySetsandSystems198620187-96.[3]BustinceHBurilloP.Vaguesetsareintuitionisticfuzzysets[J].FuzzySetsandSystems199679403-405.[4]GauWLBuehrerDJ.Vaguesets[J].IEEETransSystManCybern1993232610-614.[5]ChenSMTanJM.Handlingmulti-criteriafuzzydecision-makingproblemsbasedonvaguesettheory[J].FuzzySetsandSystems1994672163-172.[6]HongDHChoiCH.Multi-criteriafuzzydecision-makingprob－lemsbasedonvaguesettheory[J].FuzzySetsandSystems2000114103-113.[7].Vague[J].200128760-65.[8].Vague[J].2004103-109.[9].Vague[J].2006247120-123.[10].[J].200620571-76.[11]LiDeng-feng.Multi-attributedecisionmakingmodelsandmeth－odsusingintuitionisticfuzzysets[J].JournalofComputerandSys－temSciences20057073-85.[12]LinLinYuanXue-haiXiaZun-quan.Multicriteriafuzzydici－sion-makingmethodsbasedonintuitionisticfuzzysets[J].JournalofComputerandSystemSciences20077384-88.[13].[J].200737578-82.[14]XuZe-shui.Intuitionisticpreferencerelationsandtheirapplicationingroupdecisionmaking[J].InformationSciences2007177112363-2379.[15].[J].200621111253-1256.A1A2A3C10.750.100.600.250.800.20C20.800.150.680.200.450.50C30.400.450.750.050.600.30《》20084436122《ns-2》“”“”139