一个具有可调变权能力的变权向量

27 1 Vol. 27 No. 1e %Control and Decision2012 M1Jan. 2012B VM ? M _ cI|: 1001-0920 (2012) 01-0082-05o1;2, 1(1.0 S/v 710071 2. B “ B725000)K1:G M _ l/B M _ ,i M _ M _ 1“ ;YVM _ M Q, p /M _ M,is M rT.KM _ pB , TV ,M _ (1959), 3, q,p V 3 =,VYK .1 o:B VM ? M _ 83(W1)BB:mXj=1wj(x) = 1;(W2) : wj(x1;x2; ;xm)1 1M (j = 1;2; ;m).5w(x)xM _ ,eM _ .MM8 maxx20;1m mXj=1xjwj(x):TM _ w(x) :(W3): wj(x1;x2; ;xm)11M xjh(j = 1;2; ;m),5w(x)M _ .TM _ w(x) :(W30) : wj(x1;x2; ;xm)11M xj9(j = 1;2; ;m),5w(x) M _ .lll2 !sj : 0;1m!0;1(j = 1;2; ;m),Ts(x) = (s1(x);s2(x); ;sm(x) :(S1) ix = (x1;x2; ;xm) 2 0;1m, xi xj,5si(x) 6 sj(x);(S2) sj(x1;x2; ;xm)1 1M (j= 1;2; ;m);(S3) _ w = (w1;w2; ;wm),w(x) l1(W1), (W2)(W3), Ow(x) = (w1s1(x); ;wmsm(x)mXj=1(wjsj(x): (1)5s(x) M _ , T(1)ws(x)BBHadamard.T|(S1) /Hq:(S10)x20;1m, xixj,5si(x)sj(x);O|(S3)(W3)(W30),5Ms(x) M _ .M _ “S %“8 H, I n “SM1( “S ),7 O I n “SF ( M _ ), D2 UM 8 .BM _, i M _ , PM _ X _ BBHadamard?/ s 5. 1 !w = (w1;w2; ;wm) _ Owj 0(j = 1;2; ;m);x 2 0;1m;w(x) = (w1(x);w2(x); ;wm(x).1) Tw(x)M _ ,5i M _ s(x) Pw(x) = (w1s1(x); ;wmsm(x)mXj=1(wjsj(x) 1Hq : x = (x1;x2; ;xm) 2 0;1m, xi xj,5wi(x)wi6 wj(x)wj;2) Tw(x) M _ ,5i M _ s(x) Pw(x) = (w1s1(x); ;wmsm(x)mXj=1(wjsj(x) 1Hq : x = (x1;x2; ;xm) 2 0;1m, xi 6 xj,5wi(x)wi6 wj(x)wj. 1) s. !w(x)M _ ,5 x 2 0;1mwj(x) 0 OmXj=1wj(x)= 1.ywj 0,# |sj(x) = wj(x).wjmXi=1wi(x)wi; (2)s(x) = (s1(x);s2(x); ;sm(x)./ s(x) M _ . n5,wj 0;wj(x) 0, T(2)0 6 sj(x) 6 1. Q,ywj(x)1 1M ,#sj(x)1 1M ,s(x)(S2).9 , zw(x) = (w1s1(x); ;wmsm(x)mXj=1(wjsj(x);yNs(x) (S3).7x 2 0;1m,xi xjH,ywi(x)=wi 6 wj(x)=wj,#si(x)sj(x) = wi(x)wi wj(x)wj6 0;s(x)9 (S1).yN l2 V, s(x) M _ .A1.D10 1 V.2) 1).21 “S %5, I n “SA1,V7 “S d ,yN1Hqwj 0(j = 1;2; ;m) . M _ B M ,M _ M Q.lll3 !x 2 0;1m;w _ Owj 0(j = 1;2; ;m), w(x)M _ ,vj(w(x) = wj(x)wjwjM _ w(x)x)1wjM,84 e %27 v(w(x) =vuut mXj=1(vj(w(x)2w(x)x)9M.Mvj(w(x)V UM wj(x) wjMM .A vj(w(x) H,M 9v xj ;vj(w(x) H,M hl xj .9MV UM _ w(x) _ ws MM 8.Ms M _ M 1T,Y, %V Y5BM K,“ Vh /M _ i,7 O/M _ 9 %M 1 p.3 MMM _ “ -/M _ BZE 5/ M_ , _ B 3M _ . YL ,G M X,vM _ l V/M _ 14. _ w =(w1;w2; ;wm),/_ w(x) = (w1(x);w2(x); ;wm(x), wj(x) = (1+fi(xxj)wj: (3): j = 1;2; ;m;x 2 0;1m; x =mXj=1(xjwj);fi 1minx20;1mmin16j6m(xjx)6fi61maxx20;1mmax16j6m(xjx):(4) 2 T(3)w(x) V M _ V UM _ .fi 0 H, w(x) M_ ;fi 0 HA wj(x) =(1+fi(xxj)wj 0;xxj 1+ xxjmaxx20;1mmax16j6m(xj x)wj 1+ xxjxj xwj = 0:ymXj=1wj(x) =mXj=1(1+fi(xxj)wj =mXj=1wj +fixmXj=1wjmXj=1xjwj= 1;#w(x) l1BB.ywj(x)=xj= fi(wj 1) 0,5w(x)M _ ;fi =0 H,A w(x) = w _ . ,1w(x) fiT a |,L ? M _ , L= vZL.9 ,T(3)M _ w(x)xjMvj(w(x) = fi(xxj),9Mv(w(x) = jfijvuut mXj=1(xxj)2; xF Zjfij.A fix s,=M _ M (Y. n5, 4 Ax (MY? p:x ( H(x1 = x2 = = xm),9Mv(w(x) = 0,N HM _ Mx s ,w(x) = w;x ( H, v(w(x)|v,N HM _ M 9 v,M X. Q,%x 20;1m,1XM vM _ w(x),1 | Pjfij v fi.Y |fi = 1minx20;1mmin16j6m(xj x)H, w(x) KvM M _ ;|fi = 1maxx20;1mmax16j6m(xj x)H, w(x) KvMM _ .4 L L L sss |D8 5 T(3)M _ M rT.1 o:B VM ? M _ 85 5 v / ,(w1), S(w2)(w3) 3 “ST S,A, B, C, D, E 5F ,V1V2sY I “S % .V1 “S “S S0.36 0.31 0.33V2 % SA 0.214 0.166 0.184B 0.206 0.220 0.182C 0.195 0.192 0.220D 0.181 0.195 0.185E 0.175 0.193 0.201 8ZE p, “f M0(x) =3Xj=1(xjwj)9 ,sYM0(A) =0:1892, M0(B) = 0:2024, M0(C) = 0:2023, M0(D) =0:1867, M0(E) = 0:1892.M B C A E D.D8 XM 8ZE B C A E D./ T(3)M _ p5,N HM “f M(x) =3Xj=1(xjwj(x): (6) % , T(4) 70:621 6 fi 640:355. |fi = 1, T(3)9 ,V3 M .V3M SA 0.351 0.317 0.332B 0.359 0.304 0.337C 0.363 0.313 0.324D 0.362 0.307 0.331E 0.365 0.309 0.326V4M SA 0.271 0.382 0.347B 0.347 0.256 0.397C 0.386 0.342 0.272D 0.380 0.284 0.336E 0.411 0.298 0.291 T(6)9 sYM(A) = 0:1888, M(B) = 0:2022, M(C) = 0:2022,M(D) = 0:1866, M(E) = 0:1890.M C B E A D. 8ZEM1, TC M, M 8ZE I n (. T XM 8ZE TM .YV9 ,M _ 9Mv(w(A) = 0:0344, v(w(B) = 0:0272, v(w(C) =0:0217, v(w(D) = 0:0102, v(w(E) = 0:0189.A M A I “S MKv, A 5 K (.V91 ,M _ A w1MKv,2:5%.T |fi = 10,5 T(3)9 V4 M . T(6)9 M(A)= 0:1852, M(B) = 0:2000, M(C) = 0:2008, M(D) =0:1863, M(E) = 0:1879.M C B E D A. 8 M1, C vM, N HM _ I n (. HM _ 9Mv(w(A) = 0:344, v(w(B) = 0:272, v(w(C) = 0:217,v(w(D) = 0:102, v(w(E) = 0:189.M _ Aw1M9Kv,25%.A , |, %T,“ %T8C % (1 p, L= f ,9F .5 PM 8ZE p “S %5 H,B1o / % ( z1 pM _ .NVM X, l/ B M _ ,i M _ V M _ _ V U, H9 M.YV s L V ,1M _ |, MrT.yNM _ B MaM M _ , ? % ( z1 p, L= vZL. ID(References)1 . “ “ M.: =Sv, 1985: 47-59.(Wang P Z. Shadow of fuzzy sets and random setsM.Beijing: Beijing Normal University Press, 1985: 47-59.)2 .y bW MV U O()J.“d , 1995, 9(3): 1-9.(Li H X. Factor spaces and mathematical frame ofknowledge representation()J. Fuzzy Systems andMathematics, 1995, 9(3): 1-9.)3 .y bW MV U O()J.“d , 1996, 10(2): 12-19.(Li H X. Factor spaces and mathematical frame of86 e %27 knowledge representation()J. Fuzzy Systems andMathematics, 1996, 10(2): 12-19.)4 .y bW MV U O()J.“d , 1996, 10(4): 110-118.(Li H X. Factor spaces and mathematical frame ofknowledge representation()J. Fuzzy Systems andMathematics, 1996, 10(4): 110-118.)5 , . M 8“ (f /J.“d Ll, 1999, 19(7): 116-118.(Zhu Y Z, Li H X. Axiomatic system of state variableweights and construction of balance functionsJ. SystemsEngineeringTheory and Practice, 1999, 19(7): 116-118.)6 b, . M _ /J. =Sv, 2002, 38(4): 455-461.(Li D Q, Li H X. The properties and construction of statevariable weight vectorsJ. J of Bejing Normal University,2002, 38(4): 455-461.)7 b,! , .1 M _ l TJ.“d Ll, 2004, 24(5):97-102.(Li D Q, Gu Y D, Li H X. Results on axiomatic definitionof state variable weight vectorJ. Systems EngineeringTheory and Practice, 2004, 24(5): 97-102.)8f , b.M % M _ XEJ. Ll M, 2009, 39(6): 93-97.(Zhang L Y, Li D Q. An ideal point approach of weightsvector in determining state variable decision makingJ.Mathematics in Practice and Theory, 2009, 39(6): 93-97.)9 b, .M rTs M _ J. e %, 2004, 19(11): 1241-1245.(Li D Q, Li H X. Analysis of variable weights effect andselection of appropriate state variable weights vector indecision makingJ. Control and Decision, 2004, 19(11):1241-1245.)10 b,yf C. M _ M rTJ.“d Ll, 2009, 29(6): 127-131.(Li D Q, Hao F L. Weights transferring effect fo statevariable weights vectorJ. Systems EngineeringTheoryand Practice, 2009, 29(6): 127-131.)11 b,a , .QM y %J.“d, 2004, 19(3): 258-263.(Li D Q, Cui H M, Li H X. Multifactor decision makingbased on hierarchical variable weightsJ. J of SystemsEngineering, 2004, 19(3): 258-263.)12 W . T4Qsy %J.“d Ll, 2006, 26(3): 25-32.(Nie M L. Hierarchy variable weight decision-making inthe selection of supply chains cooperatorsJ. SystemsEngineeringTheory and Practice, 2006, 26(3): 25-32.)13 =z, ,I,.M QsEJ.“d Ll, 2010, 30(4): 724-731.(Li C H, Sun Y H, Jia Y H, et al. Analytic hierarchy processbased on variable weightsJ. Systems EngineeringTheoryand Practice, 2010, 30(4): 724-731.)145.BM _ # J. Ll M, 2008, 38(20): 134-138.(Xu Z Z. The construction and application of a new variableweight vectorJ. Mathematics in Practice and Theory,2008,