一类不确定性决策问题的变权分析方法

371郑州大学学报(理学版)Vol.37No.120053J.ofZhengzhouUniv.(Nat.Sci.Ed.)Mar.2005:20040815;:20040312:,BK2003211;,2003120012.:(1959-),,,,;E-mail:[e-mail].罗　党1,3,　王　伟2,　吕　健3(1.210016;2.450052;3.450008):,,.,,,,,..:;;;;:C934;N945:1671-6841(2005)01-0099-050[1],[2],,[37].,[3].,,.,,,.,,,.,.,..[8],..[9],.[4],....1xm[0,M],jtjxqj,tj[0,M],tj=M;tj=0,xqj.j=j(t),t[0,M](j=1,2,,m),:(i)j(t)[0,M];(ii)j(t)[0,M]j(t)0().j=j(M),j=j(0),　100郑州大学学报(理学版)37wj=wj(t1,t2,,tm)=j(tj)mk=1k(tk),j=1,2,,m(1)wj(t1,t2,,tm):(iii)wj,wj(0,1),mj=1wj=1;(iv)j,wjtj(dwj(tj)dtj0);(v)0=kjk(tk),a0=-10kjk(tk)tk,*j=kjwk,*j=kjk,U(t)=[0a0+j(t)t]/[0+j(t)](2)[8],j,mk=1wktktjtU(tj)v0tjj(t)-j(t)[0+j(t)]/0(t-v0).wj=wj(M,M,,M),w-j=(M,,M,0,M,,M)=j(0)/[j(0)+kjk(M)],j=1,2,,mqjwj,mj=1wj=1.(1)w=(w1,w2,,wm).,wj,w-j(j=1,2,,m),j=j(M)=wj(j=1,2,,m),(1)wj,w-j-j=j(0)=w-jkjwk/[1-w-j],j=1,2,,m(3)j(t)djdt=-wj*jMkj-1tkjj(0)=-j,j(M)=wj(4)j(t)=wjMkj-1*jt1-kj1-kj+-j(5),kj=1--j-wjwj*j,(1)wj(t1,t2,,tm)wjtj,mj=1wjtjtj(j=1,2,,m).,,,.G=X,Q,A~(),X={x1,x2,,xn},Q={q1,q2,,qm},A~()=[(ij,ij)]nm,(ij,ij)xiqjijij(i=1,2,,n;j=1,2,,m),0ij1,mj=1ij=1,0ij1,G=X,Q,A~().22.1wj(j=1,2,,m)A~()=[(ij,ij)]nm.1罗　党等:一类不确定性决策问题的变权分析方法101,,().t1,t2,,tm,y,y=f(t1,t2,,tm);t1,t2,,tm!t1,!t2,,!tm,∀t1,∀t2,,∀tm;y!y,∀y,!t1,!t2,,!tm,∀2ylim=mj=1(ftj)2∀2tjlim(6)xiqjij(i=1,2,,n;j=1,2,,m),jqjHj=-1lnnni=1ijlnij,j=1,2,,m(7)Hj,jqjj=1-Hjm-mk=1Hk,j=1,2,,m(8)jjqj.xiqjijij(7),(6)jHj#Hj:#H2j=1(lnn)2ni=1[(lnij+1)ij]2,j=1,2,,m(9)#Hj(8),(6)jqjjj:2j=1(m-mk=1Hk)4#Hj(kjHk-m+1)2+(1-Hj)2kj#H2k,j=1,2,,m(10)w~()=[(1,1),(2,2),,(m,m)].wj=j,w-j=(j+j)1,wj(j=1,2,,m).2.2G=X,Q,A~(),X={x1,x2,,xn},Q={q1,q2,,qm},A~()=[(ij,ij)]nm.1ij(i=1,2,,n;j=1,2,,m)(7)Hj(j=1,2,,m);2Hj(8)j(j=1,2,,m);3ijij(9)Hj#Hj(j=1,2,,m);4Hj#Hj(10)jj(j=1,2,,m);5wj=j,w-j=(j+j)1wj(j=1,2,,m);6(2)(3)*j,-j,(5)j(t)(j=1,2,,m),t[0,1],(5)M=1;7,(11)xiqjtij:tij=max{0,ij-12ij}(i=1,2,,n;j=1,2,,m)(11)8j(t)(1)wj(j=1,2,,m);9(6)(7)ti=mj=1wj(ti1,ti2,,tim)tij(i=1,2,,n),ti,.3[4].,,5　102郑州大学学报(理学版)37x1,x2,,x5,8(),q1,q2,q3,q4,q5,q6,q7,q8.1,.1灰色模糊决策矩阵q1q2q3q4q5q6q7q8x1(0.1481,0.0202)(0.1657,0.0128)(0.2647,0.0266)(0.2817,0.0308)(0.1290,0.0293)(0.2184,0.0103)(0.1250,0.0284)(0.2000,0.0256)x2(0.3111,0.0558)(0.2039,0.0175)(0.1471,0.0265)(0.1409,0.0116)(0.1290,0.0293)(0.1724,0.0103)(0.2500,0.0282)(0.1430,0.0258)x3(0.1778,0.0262)(0.2256,0.0203)(0.1471,0.0265)(0.1517,0.0129)(0.2581,0.0292)(0.1954,0.0103)(0.2500,0.0282)(0.1714,0.0256)x4(0.1556,0.0216)(0.2121,0.0185)(0.2353,0.0264)(0.2465,0.0258)(0.2903,0.0296)(0.2069,0.0103)(0.2188,0.0280)(0.2286,0.0256)x5(0.2074,0.0327)(0.1928,0.0161)(0.2059,0.0263)(0.1793,0.0164)(0.1935,0.0289)(0.2069,0.0103)(0.1563,0.0281)(0.2571,0.0258)2.2,Hj,j,Hj#∃j,jjwjwj,w-j(j=1,2,,m),6-j,*jj(t),t[0,1](j=1,2,,m),7tij(i=1,2,,n;j=1,2,,m),2.8wij(i=1,2,,n;j=1,2,,m),3.2决策矩阵A=(tij)5×8q1q2q3q4q5q6q7q8x10.13800.15930.25140.26630.11430.21270.11080.1872x20.28320.19510.13380.13510.11430.16720.23590.1301x30.16700.21540.13380.14520.24350.19020.23590.1586x40.14480.20280.22210.23360.27550.20170.20480.2158x50.19100.18470.19270.17110.17900.20170.14220.24423权重矩阵(wij)5×8q1q2q3q4q5q6q7q8x10.17600.08560.11920.15460.21440.02400.13730.0943x20.17670.08530.11550.15060.21360.02390.14110.0933x30.17010.08480.11470.14630.22730.02370.14010.0930x40.16750.08400.11600.14980.22870.02350.13780.0927x50.17210.08520.11690.14860.22120.02380.13760.0946ti:t1=0.1707919,t2=0.1763174,t3=0.1909166,t4=0.2180187,t5=0.1836227.t4t3t5t2t1,x4x3x5x2x1,x4.4,,.,.[4],,..1罗　党等:一类不确定性决策问题的变权分析方法103:[1],..:,1996.[2],..,1993,8(1):2529.[3].:[].:,2002.[4],..,2003,21(1):101104.[5],..,2001,9():174177.[6],..,2002,21(1):7375.[7],..,2000,14(4):5052.[8],..:,2002.163176.[9]LinSifeng,LinYi.AnIntroductiontoGreySystems:Foundations,MethodologyandApplications.SlipperyRock,IIGSSAcademicPublisher,1998.AnAnalysisMethodofVariableWeightsforUncertainDecision-makingProblemLuoDang1,3,WangWei2,LJian3(1.CollegeofEconomicsandManagement,NanjingUniversityofAeronautics&Astronautics,Nanjing210016,China;2.BusinessSchool,ZhengzhouUniversity,Zhengzhou450052,China;3.InformationEngineeringDepartmentofNorthChinaInstituteofWaterConservancyandHydroelectricPower,Zhengzhou450008,China)Abstract:Basedongreysystemtheoryandfuzzymathematics,andintermsofgrayfuzzynumbers,theexpressionoftheuncertaintythatisincludedinmultipleattributesdecision-makingisdiscussedandthedefinitionofmultipleattributesdecision-makingisgiven.Usinganalysismethodsandtechniques,andcombiningthevariableweightsmethodswiththeerroranalyticalmethodsofentropyweights,analgorithmforgreyfuzzymultipleattributesdecision-makingisdeveloped.Itismorepreciseandreliablethanthosemethodsusedbeforesinceitsbasicweightandupperboundaredirectlydeterminedbygreyfuzzydecision-makingmatrix.Thisapproachprovidesanewwayfortheresearchinuncertainmultipleattributedecision-making.Thegivenexampleprovesthealgorithm'sfeasibility.Keywords:greyfuzzydecision-makingmatrix;multipleattributedecision-making;variableweight;entropy;errorpropagation