状态变权的公理化体系和均衡函数的构造

199977朱勇珍,李洪兴(,100875),,.;;;AxiomaticSystemofStateVariableWeightsandConstructionofBalanceFunctionsZHUYongzhen,LIHongxing(DepartmentofMathematics,BeijingNormalUniversity,Beijing100875)AbstractAnewdefinitonofstatevariableweightsisgivenandsomepropertiesarediscussed.Thensomeinterestingexamplesareintroduced.Atlasttwokindsofusefulbalancefunctionsarestudied.Keywordsconstantweights;variableweights;statevariableweigths;balancefunc-tions1[4].[1,2,3],.,W0=(w1,,wm)S(X)=(S1(X),,Sm(X))Hadamard;S(X)(m)B(x1,,xm),GradB(X)=S(X).,([5]).,,.,;,.21[1]W0=(w1,,wm)(0,1]m(),:mj=1wj=1.2[1]W:[0,1]m(0,1]m,W(X)=(w1(X),,wm(X)),:w.1):mj=1wj(x1,,xm)=1;w.2):j(1jm),wj(x1,,xm)xk(k=1,,m);:1998-11-03:(69474014)w.3):wj(x1,,xm)xj,w.3):wj(x1,,xm)xj.Ww.1),w.2)w.3),W;Ww.1)w.2)w.3),W.:2,,[2].3[1]S:[0,1]m(0,1]m,XS(X)(S1(X),,Sm(X)),:s.1)Sj(ij(X))=Sj(X),ij(x1,,xi,,xj,,xm)=(x1,,xj,,xi,,xm);s.2)xixjSi(X)Sj(X);s.3)Sj(x1,,xm);s.4)W0=(w1,,wm),W(X)=W0S(X)mj=1(wjSj(X))(1)W(X)2,S;w.1)w.2)w.3),S;w.1)w.2)w.3),S.4[1]B:[0,1]mR,gradB=!B!x1,,!B!xm;gradB(),B().1[1]B1(X)=mj=1xjB2(X)=mj=1xj,B3(X)=1mj=1xj(01),.2B4(X)=mj=1(e-e-xj),.33s.1),,(5).5S:[0,1]m(0,1]m,S(X)(S1(X),,Sm(X))m,:S1):xixjSi(X)Sj(X);S2):Si(X)xi,kiwkSk(X)xi,X(1)=(x1,,x(1)i,,xm)X(2)=(x1,,x(2)i,,xm),x(1)ix(2)iSi(X(1))Si(X(2))kiwkSk(X(1))kiwkSk(X(2))(2)wk(k=1,,m).1S1;S2,.S1S2.2S(X)Si(X),S.S.,,5.1Sm,W0=(w1,,wm),(1)W(X),W(X)(2).2,w.1w.2.w.3.X(1)=(x1,,x(1)j,,xm),X(2)=(x1,,x(2)j,,xm),x(1)jx(2)j,A(x)wjSj(X)wjSj(x1,,xj-1,x,xj+1,,xm)B(x)ijwiSi(X)ijwiSi(x1,,xj-1,x,xj+1,,xm)1177wiwi/ijwi0ijwi=1.B(X){Si(X)ij}.(1)wj(x)=A(x)/(A(x)+B(x)ijwi)(3)S2,A(x)x,B(x)x;x(1)jx(2)j,B(x(2)j)A(x(1)j)B(x(1)j)A(x(2)j),A(x(1)j)/(A(x(1)j)+B(x(1)j)ijwi)A(x(2)j)/(A(x(2)j)+B(x(2)j)ijwi)wj(X)=wjSj(X)/mi=1wiSi(X)xj;w.3.4,().2g(t)[0,1],B1(x1,,xm)mj=1g(xj),B1(X)[0,1]m:g(t)g(1)0.:B1(X)(,),Si(X)=g(xi),S(X)gradB1();g(1)0.g(t).,t1,t2[0,1],t1t2,X0(t1,t2,0,,0)[0,1]m,S1S1(X0)S2(X0),g(t1)g(t2).t1,t2g(t)[0,1].:S(X)=(g(x1),,g(xm)),g(t)g(1)0,S1S2.,xi,xj,xixj,Si(X)=g(xi)g(xj)=Sj(X),S1.,S(X)=gradB1,Si(X)xi,jiwjSj(X)=jig(xj)xi,xi,S2.,xi,0g(1)g(xi),g(xi)(0,+),S(X)(0,+)m,S(X).g(t)[0,1],B1(X)mj=1g(xj)g(1)0g(t)0.3h(t)[0,1],B2(X)mj=1h(xj),B2(X)h(t)h(t)0.:S(X)=gradB2(X),S(X)(),S(X),h(t)0;Si(X)=h(xi)jih(xj),Si(X)xih(xi)xi[0,1].:S(X)=(h(x1)i1h(xi),,h(xm)imh(xm)),X=(x1,,xm),xixj,h(t)[0,1],h(xi)h(xj);h(xi)h(xj),h(xi)h(xj)h(xj)h(xi),Si(X)=h(xi)h(xj)ki,jh(xk)h(xj)h(xi)ki,jh(xk)=Sj(X)S1.,h(xi)Si(X)=h(xi)jih(xj),Si(X)xi.,jiwjSj(X)=h(xi)(jiwih(xj)ki,jh(xk))(131)11819997[1](IDAR-338).CIMS,1992[2]HubeleNFel.Automation:thechallengeforSPC.Quality,1987,26(3):1422[3]DovichRA.Small-lotSPCreally!MachineandToolBlueBook,Dec.1988:1214[4]SaltiMM,StathamA.AReviewoftheLiteratureontheUseofSPCinBatchProduction.QualityandReliabilityEngineeringInternational,1994,10:4961[5]..CIMS,:1992[6]AlexanderSMandJagannathanV.Advisorysystemforcontrolchartselection.ComputerandIn-dustrialEngineering,1986,10(3):171177[7]TsuangKuoandAnilMital.Qualitycontrolexpertsystems:areviewofpertinentliterature.Jour-nalofIntelligentManufacturing,1993,(4)[8],..,1997,(1):133137[9]AT&T.StatisticalQualityControlHandbook,DelmarPrintingCompany,CharlotteN.C,1985[10]JillASwiftandJoeHMize.Out-of-controlPatternRecognitionandAnalysisforQualityControlChartsUsingLisp-basedSystems.ComputersInd.Engng.,1995,28(1):8191(118)h(t)tjiwih(xj)ki,jh(xk)xi,jiwjSj(X)xi,S2.[1].().,1995,9(3):19[2].()Weber-Fechner.,1996,10(3):1219[3],..:,1996[4]..:,1985[5]..,1997,17(4):58741317