群决策中多阶段多元判断偏好的集结方法研究朱建军

第23卷第7期Vol.23No.7控制与决策ControlandDecision2008年7月Jul.2008:2007-05-10;:2007-08-13.:(70473037,70701017);(2005038575);([2005]255);(BR2007020).:(1976)),,,,,;(1955)),,,,,.:1001-0920(2008)07-0730-05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:AAggregationapproachofmultiplestagesmultiplejudgmentpreferencesstylesingroupdecision-makingZHUJian-jun1,LIUSi-feng1,LIHong-wei2,TIANFei1(1.CollegeofEconomicsandManagement,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,China;2.CollegeofEconomicsandManagement,ShandongUniversityofScienceandTechnology,Qingdao266510,China.Correspondent:ZHUJian-jun,E-mail:[e-mail])Abstract:Aproblemofaggregationapproachofmultiplestagesmultiplejudgmentpreferencestylesisstudiedingroupdecision-makingprocess.Multiplepreferencesaretranslatedintosingleonepreferencestylebasedonthereciprocalcomparisonmatrixandcomplementarymatrixtranslationformula.Theweightofthedecision-makerissuggestedaccordingtotheconsistencylevelofthedecisionpreferenceandthedeviationoftheindividualandthegroup.Theweightofthedecision-stageispresentedbasedontheprioriinformation.Followingthat,themultiplestagesandmultiplepreferencesareaggregatedintothegrouppreference.Keywords:Groupdecision-making;Multiplestages;Multiplepreference;Aggregation1引言,,[1-3].,.,,,.,.[4-8],.:1),;2),,,,[9-12].,.2多阶段多元判断偏好的集结模型2.1[1]:DOI10.13195/j.cd.2008.07.12.zhujj.024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=tFti=1CRki,k=1,2,,,m.(2)1ekCR=mink=1,,,mCRkCRkEmk=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):.Ej=1(wij-wkij)2,minQ=Ej,k(wij-wkij)2,i=1,2,,,t;P1:Enj=1wij=1,i=1,2,,,t;wij\0,i=1,2,,,t,j=1,2,,,n.1P1w*ij,w*ij=Emk=1wkijm.证明Qc=Ej,k(wij-wkij)2-K(1-Enj=1wij),5Qc5wi1=2Ek(wi1-wki1)-K,s5Qc5win=2Ek(win-wkin)-K,5Qc5K=1-Enj=1wij.5Qc5wi1=0,,,5Qc5win=0,5Qc5K=0,w*ij=Emk=1wkijm,i=1,2,,,t.P1,w*ij.t1,ikw*ijdki=Enj=1(w*ij-wkij)2,i=1,2,,,t,k=1,2,,,m.(3)k,iI{1,2,,,t}dk=tFti=1dki,k=1,2,,,m.,,edk=mink=1,,,mdkdkEmk=1mink=1,,,mdkdk.ekCRedk(ekCR,edk),:pek=(Bdedk)(BCRekCR)Emk=1(Bdedk)(BCRekCR),k=1,2,,,m.(4):BdBCR731控制与决策第23卷,Bd+BCR=1.Bd\BCR,;,.,Bd=BCR.2pek.pek,iI{1,2,,,t}wij,minEj,kpek(wij-wkij)2,i=1,2,,,t;P2:Enj=1wij=1,i=1,2,,,t;wij\0,i=1,2,,,t,j=1,2,,,n..2P2wcij=Emk=1pekwkij,i=1,2,,,t,j=1,2,,,n.21.2.3ijwij,i=1,2,,,t,j=1,2,,,n.t.,twj=Eti=1wijt,j=1,2,,,n,(5)Enj=1wj=1.,pi(i=1,2,,,t):1),,pi[pi+1;2)Ai,Aipi[pi+1,Ai\1;3)(di=Ejpi(wj-wij)2,i=1,2,,,t).,piminEi,jpi(wj-wij)2;P3:Aipi[pi+1,Ai\1,Eti=1pi=1,pi\0,i=1,2,,,t.wj((5)).,wcjP4,minEi,jpi(wcj-wij)2;P4:Enj=1wcj=1,wcj\0,j=1,2,,,n.piP3.3P4wcj*=Eti=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):85-91.[2].AHP[J].,1999,19(7):97-101.(XuZS.StudyontherelationbetweentwoclassesofscalesinAHP[J].SystemsEngineering-theory&Practice,1999,19(7):97-101.)[3],.[J].,2005,20(2):211-215.(ChenY,FanZP.Studyontheadversejudgmentproblemforgroupdecisionmakingbasedonlinguisticjudgmentmatrices[J].JofSystemsEngineering,2005,20(2):211-215.)[4]ChiclanaF,HerreraF.Integratingthreerepresentationmodelsinfuzzymultipurposedecision-makingbasedinfuzzypreferencerelations[J].FuzzySetsandSystems,1998,97(1):33-48.[5]DelgadoM,HerreraF,HerreraV.Combiningnumericalandlinguisticinformationin-groupdecision-making[J].InformationSciences,1998,107(1):177-194.[6],.OWG[J].,2003,6(1):32-36.(FanZP,JiangYP.Approachtogroupdecision-makingwithdifferentformsofpreferenceinformationbasedonOWGoperators[J].JofManagementSciencesinChina,2