网络决策分析的积因子方法

200499:100026788(2004)0920090208(;,100089):,()LL:;;:N945.25:ATheProductMethodofAnalyticNetworkProcessLIUQi2zhi(AirForceAcademy;InformationSchool,RenminUniversityofChina,Beijing100089China)Abstract:Inthispaperanewdecisionmethodforanalyticnetworkprocessisproposed.Inthemethodtheconceptsofdirectedgraphandrelatedmatrixisused.ItisprovedthatthemethodisexpandedfromProductAHP(inthemethodwhensynthesizinghierarchyresults,productnotsumisused)andcandealwithgeneralnetworkstructuredproblem.Keywords:AHP(analytichierarchyprocess);ANP(analyticnetworkprocess);decisionmethod:2003210230:(1945-),,,,,,Email:[e-mail].1(AnalyticHierarchyProcessAHP),,,L,(AnalyticNetworkProcessANP)L,,L,LT.L.Saaty,,L,LT.L.Saaty,L,,[1,2]L[3,4]LT.L.Saaty,L,,,,L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.22.1L,,L,L:,,;,LZAB1B2,,B1B2A,AB1B2ZAB1B2,B1B2A,()Z,,,Z:,,Z,,,,Z2.2,(,,):1)Z,,Z,.2)Z,,ZZ,Z3),Z,,,Z,Z4)Z,,,Z,,Z1199©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.2.3,2)3),,:1)ZZ2)Z(),()Z,,Z2,,Z,,Z,:1)Z,,Z2)Z,Z,,:É;ÊZ3,ZZ,ZZ3.1,Z,U1,U2,,Un,Ui,Uj,Z1-9,,Z11-9135792,4,6,8,n,1,Z3.2,,,,,Z,,1Z,2920049©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.Z,,Z,Z,,Z3.13.2Z4,,Z4.1,,Zk-1p=(x1,x2,,xk),xkpx1:a1a2ak-1,ai(xi,xi+1)Z4.2,:A=[aji],aji:ij,aji(i,j);i=j,iaii=0;i=j,iaii=1Z,A,1,ATMarkovZiaii=1,,0,1Z,i,aii=0,aii=1Z4.3A=[aij],B=[bij],C=[cij],C=ABcij=6nl=1ailblj.Ak[dij]=Ak,,dij:1)j,dijjik;2)j,dijjikZ4.44.4.1()Zl+1,,Z(),,:399,,,,L©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.A=0000A10000A20000AlI.0ZAiii+1ZAl,Al=000000000000AlAl-1A1AlA2AlI.All+1lZAll+1Z:4.1,limsAs=Al4.4.2Z:1(),(),Z2r(x)xZ,(x,y),:r(y)=r(x)+1Z(x,y)Zxk,yj,yk+1y,jkZ(x,y)j-k-1,(x,x1xj-k-1,y),(x,x1)(x,y),1ZZ.4.2Z,i1,i2,,iss,0s(0,i1),(0,i2),,(0,is),a0i1=a0i2==a0is=1ös,Z:4.3Z,Z2Z(A11,A12,A13)A1,A2,A3B1,(A21,A22,A23)A1,A2,A3B2,(b1,b2)B1,B2G,4920049©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.A=000000b100000b2000000a11a211000a12a220100a13a23001,G,B1,B2,A1,A2,A3,ZA2=000000000000000000c1a11a21100c2a12a22010c3a13a23001,(c1,c2,c3)T:c1c2c3=a11a12a13a21a22a23b1b24.5AMarkov,MarkovlimsAs.B=[bij],limAs,B,limAs,BAZZi,j1,j2,,jrx1,x2,,xr,i,:fi(x1,x2,,xr)=xbij11xbij22xbijrr.5,:,,:5.1,Z()Z,Z:()(,)ZZ(),,Z,,Z5.2,Z,,ZZ,Z599©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,Z5.3,,Z,Z,,(Delphy)Z,,Z,,Z,Z,A=[aij],B=[bij]Zx1,x2,,xr,i,:fi(x1,x2,,xr)=xbij11xbij22xbijrr5.4,Z,,Z66.1,((x1(1),x2(1),,xr(1))((x1(2),x2(2),,xr(2)):6.1,,,f(k1x1(1),,krxr(1))f(k1x1(2),,krxr(2)=f(x1(1),,xr(1))f(x1(2),,xr(2),,Z,Z,,,:6.1,Z1,,,,:6.2,Z,,Zf,,ki0,xi(1)0,xi(2)0,i=1,2,,rf(k1x1(1),,krxr(1))f(k1x1(2),,krxr(2))=f(x1(1),,xr(1))f(x1(2),,xr(2)),f(x1,,xn)=AxA11xArr.A,A1,,ArZ[3]Z,Z:6.2,(),Z6.2,Z6.3,,Z6920049©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.7L,L:[1]LiuQizhi,WangQin.Productmethodofanalytichierarchyprocess[J].Asia2PacificJournalofOperationalResearch,1991,(8):135-145.[2]LiuQizhi,WangQin.ProductmethodofAHP[A].ProceedingsofInternationalSymposiumontheAnalyticHierarchyProcess[C],Tianjin,China,1988,225-231.[3].[J].,1995,(10),61-70.LiuQizhi.RankpreservationpropertyofproductAHP[J].SystemsEngineeringJournal(Chinese),1995,(10):61-70.[4]LiuQizhi.ProductAHPandItsProperties[A].Proceedingsofthe6thInternationalSymposiumonAnalyticHierarchyProcess(ISAHP)[C].Bern2Switzerland,2001.341-348.[5]SaatyTL.TheSevenpillarsofanalytichierarchyprocess[A].ProceedingsoftheFifthInternationalSymposiumonAnalyticHierarchyProcess[C].Kobe,Japan,1999,20-23.[6]SaatyTL.AnoteonmultiplicativeoperationsinAHP[A].ProceedingsofInternationalSymposiumontheAnalyticHierarchyProcess[C].Tianjin,China,1988,82-86.[7]SaatyTL.Observationsonmultiplicativecompositionintheanalytichierarchyprocess[A].Proceedingsofthe3rdInternationalSymposiumonAnalyticHierarchyProcess[C].WashingtonDC,USA,1994,169-174.[8]BarzilaiJ.OnthederivationofAHPproperties[A].ProceedingsoftheFourthInternationalSymposiumontheAnalyticHierarchyProcess[C].Burnaby,B.C.Canada,1996,244-250.[9]RamanathanRGroup.DecisionmakingusingmultiplicativeAHP[A].ProceedingsoftheFourthInternationalSymposiumontheAnalyticHierarchyProcess[C].BurnabyBC,Canada,1996,262-272.[10].[M].:,1988.XuShubo.ThePrincipleofAHP.TianjinUniversityPress(Chinese),Tianjin,1988.[11],.[M].:,1990.WangLianfen,XuShubo.TheIntroductiontoAHP(Chinese).ChinaRenminUniversityPress,Beijing,1990.[12],.[J].,1992,(3):63-70.ZhaoWei,JiangBo.RecentDevelopmentofAHP[J].MathematicsinPracticeandTheory(Chinese),1992,3:63-70.[13]SaatyTL,LGVargas.DecisionMaking[M].RWSPublication,Pittsburgh,1994.(89)[3],.[J].(),2002,15(2):47-50.WEIPing.ZHANGYuan.Testpapergenerationwithgeneticalgorithm[J].JournalofNINGBOUniversity(NSEE),2002,15(2):47-50.[4],,.[J].,2002,26(3):193-196.LIUBin,JINTao,CHENDa2ping.Applicationofagenetialgorithmtocomposingatestpaper[J].JournalofYanshanUniversity,2002,26(3):193-196.[5]TakahashiK.&YamadaT.Applicationofanimmunefeedbackmechanismtocontrolsystems[J].JSMEInternationalJournal,SeriesC,1998,41(2):184-191.[6]NikolaevNI,IbaH,SlavovV.InductiveGeneticProgrammingwithImmuneNetworkDynami