具有方案偏好信息的灰色多属性决策方法

473()Vol.47No.320085JournalofXiamenUniversity(NaturalScience)May20081,2,33(1.,2.,450011;3.,,361005):2007205222:(60704042),(0524490021),(072102340009),(2007BJJ014),(2007110020),9853:[e-mail]:.,,,..:;;;:TP27:A:043820479(2008)0320323205,()[1-2].,.,,,,[3],,[4][3].,,...,,,.,.:,,;,,;,,.,[5-9],,,,11[10]()a(á)[a,b],b(á)[c,d],a,b,c,d,a(á)+b(á)[a+b,a+b],a(á)-b(á)[a+b,a+b],a(á)b(á)[min{ab,ab,ab,ab},max{ab,ab,ab,ab}],a(á)/b(á)[min{a/b,a/b,a/b,a/b},max{a/b,a/b,a/b,a/b}],a(á)[a,a],0,R[a,a],0,R.2[5]()a(á)[a,…a],b(á)[b,…b],la=…a-a,lb=…b-b,a(á)b(á)p(a(á)b(á))=min{la+lb,max{…a-b,0}}la+lb(1)3[5]()p=(pit)nm,pit=p(rij(á)rtj(á))rij(á),i,t=1,2,n.ui=1n(n-1)(nt=1pit+n2-1)(2)22.1piijsisj,(AHP)[2]19si:(i)sisj;,piij=1-19;(ii)sisj;,piij=1-17;(iii)sisj;,piij=1-15;(iv)sisj;,piij=1-13;(v)sisj;,piij=1-12;(vi)sisj;(i)(ii),piij=1-18;(vii)sisj;(ii)(iii),piij=1-16;(viii)sisj;(iii)(iv),piij=1-14;piij,piij+pjij=1pjij.2.2A={A1,A2,,An},G={G1,G2,,Gm},w=(w1,w2,,wm)T0wk1,mk=1wk=1.AiGjaij(á)(i=1,2,,n;j=1,2,,m),A=aij(á)nm,i=1,2,,n;j=1,2,,m.,,A,B=(bik(á))nm,bik(á)[bik,…bik].,Aidi(á)=mk=1bik(á)wk,i=1,2,,n(3)AiAj:piij(á)=mk=1bik(á)wkmk=1(bik(á)+bjk(á))wk=[mk=1bikwk,mk=1…bikwk][mk=1(bik+bjk)wk,mk=1(…bik+…bjk)wk](4)piij(á)[mk=1bikwkmk=1(€bik+€bjk)wk,mk=1€bikwkmk=1(bik+bjk)wk]=[piij,Špiij](5)i,j=1,2,n.piij,Špiij.,,,giij(w)(á)=piij-piij(á),giij(w)(á)[piij-Špiij,piij-piij]=[giij(w),Šgiij(w)](6)giij(w),Šgiij(w).,giij(w)(á)Hiij(w)=piijmk=1(bik+bjk)wk-mk=1…bikwk,i,j=1,2,,n.”Hiij(w)=piijmk=1(…bik+…bjk)wk-mk=1bikwk,i,j=1,2,,n(7),piijŠpiij,giij(w)(á)giij(w)Šgiij(w).I:minH(w)=ni=1nj=1[piijmk=1(bik+bjk)wk-mk=1…bikwk]2,s.t.mk=1wk=1,wk0,k=1,2,,m(8)II:min”H(w)=ni=1nj=1[piijmk=1(…bik+…bjk)wk-423()2008mk=1bikwk]2,s.t.mk=1wk=1,wk0,k=1,2,m(9)I:LagrangeL=nj=1nj=1[piijmk=1(bik+bjk)wk-mk=1…bikwk]2+2(mk=1wk-1),,Lagrange,5L5wk=0,k=1,2,,m.ni=1nj=1{mk=1[piij(bik+bjk)-…bik]wk}[piij(bik+bjk)-…bik]+=0,k=1,2,,m(10)(8),(10)m+1w1,w2,,wm,m+1,QeeT0w=01(11)e=(1,1,,1)T,Q=(qlk)mm.Q:qlk=ni=1nj=1[piij(bik+bjk)-…bik][piij(bik+bjk)-…bik],j,k=1,2,,m.(11),giij(w)w3=Q-1eeTQ-1e(12)II,w3=Q-11eeTQ-11e(13)e=(1,1,,1)T,Q1=(qlk)mm,Q1:qlk=ni=1nj=1[piij(…bik+…bjk)-bik][piij(…bik+…bjk)-bik],l,k=1,2,,m(14)w3Šgiij(w).(12)(13)w3w3IIIwk0.,w3,w3,w3w3,,w3w3.3:(i)w3,;(ii)w3,;(iii)w3=w3+(1-)w3(01),,=0.5.,:w=(w1,w2,,wm)T.,:1:A=(aij(á))nm,,B=(bik(á))nm;2:p=(piij)nn;3:w=(w1,w2,,wn)T,(4)piij(á),III,w3w3w3,,IIIw3w3;4:w=(w1,w2,,wm)T,(3)Aidi(á)(w)=mk=1bik(á)wk,i=1,2,,n;5:(1)p=(pit)nn,pit=p(dij(á)dtj(á)),i,t=1,2,n;j=1,2,,m.(2)ui,ui,.3[11],Ai(i=1,2,,5),Gj(j=1,2,3,4),G1;G2;G3;G4;:G1;G2;G3,G4.G270,G3[20,30].5,A=(aij(á))54A=[30,40][65,75][20,35][50,55][35,40][60,64][30,35][70,80][70,75][65,75][25,35][150,155][60,80][79,80][35,40][100,170][55,85][70,80][10,19][95,200]5233:jGj,j=1,2,3,4.(i)A:1)[5]bij=aij-aýj…a3j-aýj,bij=aij-aýj…a3j-aýj;2)[5]bij=a3ij-aij…a3j-aýj,bij=a3j-aij…a3j-aýj,…a3j=max1in{aij},aýj=min1in{aij},j=1,2,,m;3):[c3,d3],[c3,c3][d3d3]c3=min1in{…aij},d3=max1in{…aij},j=1,2,,m.bij=12[aij-c3d3-c3+aij-c3+d3-…aijd3-c3+…aij-d3];x[c3,d3],x[aij,…aij],…bij=1…bij=1-12c3-aijd3-c3+…aij-d3d3-c3;4),a3,:bij=1-max(aij-a3,…aij-a3)maxjaij-a3+maxj…aij-a3,…bij=1-min(aij-a3,…aij-a3)maxjaij-a3+maxj…aij-a3.B=[0.8181,1][0.75,0.75][0.2381,1][0,0.0333][0.8182,0.9091][0.5,0.7][0.3214,0.75][0.1333,0.2][0.1819,0.2727][0.75,0.75][0.2857,1][0.6667,0.7][0.0909,0.4545][0.5,0.55][0.2778,0.5833][0.3333,0.8][0,0.5455][0.5,1][0.2593,0.65][0.3,0.5](ii)p=(piij)55p=1/26/74/56/71/21/71/21/43/41/61/53/41/24/53/41/71/41/51/21/51/25/61/44/51/2=0.50.85710.80.85710.50.14290.50.250.750.16670.20.750.50.80.750.14290.250.20.50.20.50.83330.250.80.5(iii)p=(piij)55,B=(bij(á))54,,,II,:w3=(0.3215,0.1587,0.2347,0.2851).(iv)w=w3=(0.3215,0.1587,0.2347,0.2851),di(á)(w)=4k=1bikáwk,d1(á)(w)[0.4379,0.6847],d2(á)(w)[0.4558,0.6364],d3(á)(w)[0.4346,0.6409],d4(á)(w)[0.2688,0.5984],d5(á)(w)[0.2257,0.7717].(v)(1),p=0.50.53560.55190.72150.57890.46440.50.52160.72050.56520.44810.47840.50.69430.55190.27850.27950.30570.50.42570.42110.43480.44810.57430.5.(2)Aiu1=0.2194,u2=0.2136,u3=0.2086,u4=0.1645,u5=0.1939.A1:A2:A3:A5:A4..4,.[1].,.:[1],.[J].,1996(3):28-32.[2].[M].:,2004.[3].[M].:,2003.[4],.[M].:623()2008,1999.[5],.[J].,2005,13(1):101-106.[6],.[J].,2005,23(4):408-412.[7]Yuwei,Zhujianjun,WuYangyun.Researchongreydeci2sion-makingapproachfortheevaluationoftheenergyefficiency[C]PPProceedingsof2007IEEEInternationalConferenceonCreySystemsandIntelligentServices.2007:774-778.[8],.[J].,2004,22(8):29-32.[9].[M].:,2005.[10],,.[M].3.:,2004.[11],,.[J].,2005,27(5):841-843.UncertainMulti2attributeDecisionMakingMethodwithAlternativeSchemePreferenceInformationLUODang1,YUNHui2ping2,WUShun2xiang33(1.CollegeofManagement&Economics,NorthChinaUniversityofWater2ConservancyandElectricPower,2.CollegeofMathematics&InformationSciences,NorthChinaUniversityofWater2ConservancyandElectricPower,Zhengzhou450011,China;3.SchoolofInformationScienceandTechnology,CenterforSystemsandControl,XiamenUniversity,Xiamen361005,China)Abstract:Thispaperstudiesmulti2attributedecisionmakingproblemwithinternalgreynumberva