群决策中多阶段多元判断偏好的集结方法研究

第23卷第7期Vol.23No.7控制与决策ControlandDecision2008年7月Jul.2008:20070510;:20070813.:(70473037,70701017);(2005038575);([2005]255);(BR2007020).:(1976),,,,,;(1955),,,,,.:10010920(2008)07073005朱建军1,刘思峰1,李洪伟2,田飞1(1.,210016;2.,266510):研究群决策过程中决策者基于多个决策阶段多种结构形式的判断偏好集结方法.基于互反判断偏好与互补判断偏好的转化公式,将多种类偏好的结构一致化;利用决策者判断偏好的一致性水平和与群体综合偏好偏差的距离,提出了确定决策者权重的方法;建立了基于决策先验信息的多阶段偏好集结的决策阶段赋权模型.根据各决策阶段的权重,将多阶段判断偏好集结成群体综合偏好.:群决策;多阶段;多元偏好;集结:C943:AAggregationapproachofmultiplestagesmultiplejudgmentpreferencesstylesingroupdecisionmakingZHUJianjun1,LIUSifeng1,LIHongwei2,TIANFei1(1.CollegeofEconomicsandManagement,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,China;2.CollegeofEconomicsandManagement,ShandongUniversityofScienceandTechnology,Qingdao266510,China.Correspondent:ZHUJianjun,Email:[e-mail])Abstract:Aproblemofaggregationapproachofmultiplestagesmultiplejudgmentpreferencestylesisstudiedingroupdecisionmakingprocess.Multiplepreferencesaretranslatedintosingleonepreferencestylebasedonthereciprocalcomparisonmatrixandcomplementarymatrixtranslationformula.Theweightofthedecisionmakerissuggestedaccordingtotheconsistencylevelofthedecisionpreferenceandthedeviationoftheindividualandthegroup.Theweightofthedecisionstageispresentedbasedontheprioriinformation.Followingthat,themultiplestagesandmultiplepreferencesareaggregatedintothegrouppreference.Keywords:Groupdecisionmaking;Multiplestages;Multiplepreference;Aggregation1引言,,[13].,.,,,.,.[48],.:1),;2),,,,[912].,.2多阶段多元判断偏好的集结模型2.1[1]:第7期朱建军等:群决策中多阶段多元判断偏好的集结方法研究aij=bijbji,i,j=1,2,,n,(1)bijij.(1),,Aki(i=1,2,,t;k=1,2,,m),ik.Aki,[1],wkijCRki(j=1,2,,n),ikj.2.2([3,13]),.,.,,.2.2.1基于一致性水平的决策者赋权[14],,.[15]:CR!0.1,,.,CR.CRki,:CRk=t∀ti=1CRki,k=1,2,,m.(2)1ekCR=mink=1,,mCRkCRk#mk=1mink=1,,mCRkCRk,k=1,2,,mk.1,t,,ekCR.2.2.2基于决策偏差的决策者赋权方法i,wij(i=1,2,,t;j=1,2,,n):.#j=1(wij-wkij)2,minQ=#j,k(wij-wkij)2,i=1,2,,t;P1:#nj=1wij=1,i=1,2,,t;wij∃0,i=1,2,,t,j=1,2,,n.1P1w*ij,w*ij=#mk=1wkijm.证明Q%=#j,k(wij-wkij)2-(1-#nj=1wij),Q%wi1=2#k(wi1-wki1)-,Q%win=2#k(win-wkin)-,Q%=1-#nj=1wij.Q%wi1=0,,Q%win=0,Q%=0,w*ij=#mk=1wkijm,i=1,2,,t.P1,w*ij.&1,ikw*ijdki=#nj=1(w*ij-wkij)2,i=1,2,,t,k=1,2,,m.(3)k,i∋{1,2,,t}dk=t∀ti=1dki,k=1,2,,m.,,edk=mink=1,,mdkdk#mk=1mink=1,,mdkdk.ekCRedk(ekCR,edk),:pek=(dedk)(CRekCR)#mk=1(dedk)(CRekCR),k=1,2,,m.(4):dCR731控制与决策第23卷,d+CR=1.d∃CR,;,.,d=CR.2pek.pek,i∋{1,2,,t}wij,min#j,kpek(wij-wkij)2,i=1,2,,t;P2:#nj=1wij=1,i=1,2,,t;wij∃0,i=1,2,,t,j=1,2,,n..2P2w%ij=#mk=1pekwkij,i=1,2,,t,j=1,2,,n.21.2.3ijwij,i=1,2,,t,j=1,2,,n.t.,twj=#ti=1wijt,j=1,2,,n,(5)#nj=1wj=1.,pi(i=1,2,,t):1),,pi!pi+1;2)!i,!ipi!pi+1,!i∃1;3)(di=#jpi(wj-wij)2,i=1,2,,t).,pimin#i,jpi(wj-wij)2;P3:!ipi!pi+1,!i∃1,#ti=1pi=1,pi∃0,i=1,2,,t.wj((5)).,w%jP4,min#i,jpi(w%j-wij)2;P4:#nj=1w%j=1,w%j∃0,j=1,2,,n.piP3.3P4w%j*=#ti=1piwij.31.3算例,4,,5,33,().,?1MD1:0.50.20.750.670.80.50.80.670.250.20.50.330.330.330.670.5,MD2:113111321/31/311/211/221,MD3:0.50.250.50.330.750.50.670.670.50.330.50.50.670.330.50.5,MD4:11/33231521/31/5121/21/21/21,MD5:12131/211/2112121/311/21.2MD1:11/311/2312111/211/32131,MD2:0.50.330.670.250.670.50.80.670.330.20.50.250.750.330.750.5,MD3:15321/511/21/21/32121/221/21,732第7期朱建军等:群决策中多阶段多元判断偏好的集结方法研究MD4:0.50.250.330.750.750.50.20.750.670.80.50.80.330.250.20.5,MD5:11/42341251/21/2131/31/51/31.3MD1:111/31/2111/21/33212231/21,MD2:0.50.750.830.750.250.50.670.50.170.330.50.330.250.50.670.5,MD3:13671/31221/61/2111/71/211,MD4:11/32331251/21/2121/31/51/21,MD5:0.50.250.330.50.750.50.50.670.670.50.50.670.50.330.330.5.Step1,CR().,4120.1,.,CR0.1.Step2.1)ekCR.,(2)1,.:3,0.356;2,5,14.2314,0.1,23,.2).,P1;,(3).,5,3.3).(4),1.,ekCRedk.MD3,0.356,;..1MD1MD2MD3MD4MD5ekCR0.0920.3150.3560.0370.200edk0.2200.2400.1230.1590.258pek0.1530.2960.2250.0830.2444)(P2),:2;3;1,;4.Step3.,,,2.,3,1,.21234di10.02620.08270.03690.00930.15520.08520.10540.10750.0690.36730.2030.0890.0840.0290.405P3,minz=0.155p1+0.367p2+0.405p3;s.t.p3∃p2∃p1,p1+p2+p3=1,p1,p2,p3∃0.p1=p2=p3=1/3.,,,3.P43w1=0.297,w2=0.320,w3=0.193,w4=0.192.,2,1,34,.733控制与决策第23卷4结论.,,.,,..(References)[1]SaatyTL.DecisionmakingwiththeAHP:Whyistheprincipaleigenvectornecessary[J].EuropeanJofOperationalResearch,2003,145(1):8591.[2].AHP[J].,1999,19(7):97101.(XuZS.StudyontherelationbetweentwoclassesofscalesinAHP[J].SystemsEngineeringtheory&Practice,1999,19(7):97101.)[3],.[J].,2005,20(2):211215.(ChenY,FanZP.Studyontheadversejudgmentproblemforgroupdecisionmakingbasedonlinguisticjudgmentmatrices[J].JofSystemsEngineering,2005,20(2):211215.)[4]ChiclanaF,HerreraF.Integratingthreerepresentationmodelsinfuzzymultipurposedecisionmakingbasedinfuzzypreferencerelations[J].FuzzySetsandSystems,1998,97(1):3348.[5]DelgadoM,HerreraF,HerreraV.Combiningnumericalandlinguisticinformationingroupdecisionmaking[J].InformationSciences,1998,107(1):177194.[6],.OWG[J].,2003,6(1):3236.(FanZP,JiangYP.ApproachtogroupdecisionmakingwithdifferentformsofpreferenceinformationbasedonOWGoperators[J].JofManagementSciencesinChina,2003,6(1):3236.)[7],,.[J].,2000,21(4):453455.(XiaoSH,FanZP,WangMG.Goalprogrammingmodelforintegratingtwoformsofpreferenceinformationingroupde