层次分析法中判断矩阵的一致性研究-李玲娟

:2009-02-15;:2009-05-22:863(2006AA01Z439);(08KJB620002);(NY207051):(1963-),,,,,(,210003):,,,,,,:;;;:TP391:A:1673-629X(2009)10-0131-03ResearchontheConsistencyoftheJudgmentMatrixinAHPLILing2juan,DOUKun(CollegeofComputer,NanjingUniversityofPostsandTelecommunications,Nanjing210003,China)Abstract:ConstructingthejudgmentmatrixwhichmeetstheconsistencyrequirementisoneofthekeyissuesofAHP.Inordertoimprovetheconsistencyofthejudgmentmatrix,studyandanalyzethefactorswhichaffecttheconsistencyofthejudgmentmatrixinAHP,anditdesignsamethodtopreprocesstheresultsofexpertsjudgment.Thismethodusesthemaximumdeviationvalueandmeansquareddevia2tiontofilterthejudgmentinformationgivenbyexperts.Ifthejudgmentmatrixhaslagerdeviationoftheconsistency,themethodwillre-seekexpertsadvicesordeletethisjudgmentinformationdirectly.Themethodcannotonlyimprovetheconsistencyofjudgmentma2trix,butalsoesteemandmakegooduseoftheinitialjudgmentinformationfromexperts.Theinstanceshowsthatthejudgmentmatrixconstructedwiththepreprocessedjudgeinformationhasbetterconsistency.Keywords:AHP;consistency;judgmentmatrix;preprocess0(AnalyticHierarchyProcess,AHP)2070,,,,,,AHP,,SattyAHP,:(ConsistencyRatio)CR0.1,,[1],,,,,,11.1An:a1,a2,,an,ai0,ai/ajiAj,aij,:1910200910COMPUTERTECHNOLOGYANDDEVELOPMENTVol.19No.10Oct.2009A=a1/a1a1/a2a1/ana2/a1a2/a2a2/anan/a1an/a2an/an=a11a12a1na21a22a2nan1an2annAaij[2]:aij0aij=1ajiaii=1(i=1,2,,n)A1A=(aij)nn,Pi,j,k=1,2,,n,aij=aikakj,A,A1A[3]:(1)rank(A)=1,max=n,W=(W1,W2,W3,,Wn);(2)aij=aikakj(,i,j,k=1,2,,n);(3)A;(4)A;(5)A,[4,5]A11aiaje0/4aiaje2/4aiaje4/4aiaje6/4aiaje8/4aiaje1/4,e3/4,e5/4,e7/4aiaj1.2,5,(5):A1=e0/4e1/4e1/4e2/4e4/41/e1/4e0/4e0/4e2/4e1/41/e1/4e0/4e0/41/e1/4e4/41/e2/41/e2/4e1/4e0/41/e2/41/e4/41/e1/41/e4/4e2/4e0/4A2=e0/4e1/4e1/4e0/4e3/41/e1/4e0/41/e1/4e2/41/e4/41/e1/4e1/4e0/41/e5/4e4/4e0/41/e2/4e5/4e0/41/e1/41/e3/4e4/41/e4/4e1/4e0/4A3=e0/4e1/4e3/4e3/4e2/41/e1/4e0/4e2/4e4/4e1/41/e3/41/e2/4e0/4e2/4e2/41/e3/41/e4/41/e2/4e0/4e1/41/e2/41/e1/41/e2/41/e1/4e0/4A4=e0/4e2/4e4/4e4/4e7/41/e2/4e0/4e1/4e5/4e2/41/e4/41/e1/4e0/41/e2/4e3/41/e4/41/e5/4e2/4e0/4e1/41/e7/41/e2/41/e3/41/e1/4e0/4A5=e0/4e1/4e2/4e4/4e5/41/e1/4e0/4e1/4e3/4e1/41/e2/41/e1/4e0/4e1/4e2/41/e4/41/e3/41/e1/4e0/4e2/41/e5/41/e1/41/e2/41/e2/4e0/4[6]:A=11.3501.7331.9162.8580.74111.1622.2261.0510.5770.86110.7792.1170.5220.4491.28411.0510.3500.9510.4720.951122.1,:(1)Awij:wij=aij/ni=1aij;(2)wijwi:wi=ni=1wij;(3)wiWi:Wi=wi/ni=1wi,W=(W1,W2,W3,,Wn);23119(4)=ni=1(AWT)inWi,CICR,CI=(max-n)/(n-1);CR=CI/RI,RI2.2AW=(01309,01222,01184,01153,01132),max=51167,CI=01042[7],RI(2),CR=0106011212345678910111213RI000.360.580.720.820.880.930.970.991.011.031.04,A,W=(01309,01222,01184,01153,01132)3,,[8],3.11,A,aij=aikakj,(i,j,k1,2,,n),aijaikakj,s,s:s=maxi,j,k|aij-aikakj|=ni=1nj=1nk=1(aij-aikakj)2n,s,3.21.2,33A1A2A3A4A5s1.7186.3891.7181.7181.7181.2682.6651.0991.2681.268,A2max=51569,CR=01198011,,,,:A=11.3671.8682.2543.0800.73211.2842.3991.3670.5350.779111.9890.4440.417111.1330.3250.7320.5030.8821AW=(01327,01236,01180,01137,01120),max=51084,CR=01029,AA,,WW,4,,,,,,:[1]SaatyTL.TheAnalyticHierarchyProcess[M].NewYork:McGraw-Hill,1980.[2],,.[J].,2007,14(1):39-43.[3].[D].:,2005.[4],.[J].,1995,15(10):43-46.[5]BeynonM.AnanalysisofpriorityvaluesfromalternativecomparisonscaleswithinAHP[J].EuropeanJournalofOper2ationalResearch,2002,140:104-117.[6]JiangYP,FanZP,WangXR.Alagrangemultiplierrank2ingmethodforthefuzzyjudgmentmatrix[C]InternationalConferenceofManagementScience&Engineeriny(ICMSE2001).Haerbin,China:[s.n.],2001.[7].[J].,2006,24(18):31-32.[8],.[J].,2007,30(19):46-48.33110: