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1996+()WeberFeChnre`’(,,100875)〔`8〕,。,。,,Weber-Feehner。;;;WebereFchner18」,:W(X)WSx()Hardarmard。W(X)=(W15,(X),…,W,S,。(X))wjs,(x)J~lW(X)=(Wl(X),,,W:,…,W)。W0SxW,S,(X)(1.1)X=(,,xZ,…,,。),(X),…,S。(X)),W=(WJ=lW:(X),…,W,(X)),Sx=(S,(X),52:Sxm()Bx(,,xZ,…,x,),gradB(x,,x:,…,x。)=S(1.2)aB~S,(X).[8]:J`B(x,,x:,…,。)?。S(X)(S;(X),S:(X),…,S,(X))Xx(,,x:,…,x),mF(x:,…,x),F(xl,…,x。)S,(x,,…,x。)·(1.3)[8〕33.2F(,,,F(,,…,x):S,(x,,…,:aBax,,x。)=U(xl,…,x,)+V(Jl,…,,)B(1.4)(1.4)B(;,…,x,。),u(x)v(x)BJ1`xJ(1.5)1995724。(69474011):()l3,U(X)o,V(X)P,P(,P),(1.5):aB,P(1.6)(1.7)dBBPx,n、ōX\X`、Jd,é(1.6)dxlX1dxldxodxZdx.—-—,—XlxxZ-—,…,Xxl`--m:`2,…。lXB=c,l,=c,nBB,·xxB:X1XB},lUJ。,(1.8)。1,:,…,、*。a_1。,,,。、。*,.,B,g,2U,·O、」、BB(x,,…,,):,},…,{、X,。,(1.9)。1.1l(.9)Pm,y,,…,;)Hy,,J~lBx(,,…,x,):`,,~IJJ~l(1.10)[8〕(4.4)。,,l11.2(1.9)p1,(y,,…,y,nl)1,,,]lf,.x,{0、JI,…,J.jJ,{1~lweJ—}~、xxj(1.11)J~1[8〕(4.2)。1.3(1.9)pma,a0,y,,…,1)-,ln“=l。(,,…,,)x:。{{“a,l}x。)(1.12)z=la1,(1.12)(1.10)。S,(1,,:::1…(1.13)x,x,,、、、,S,(,,S,(xl,,Jx’Xx__。l1S,(x,,…,x。)S,(x,,…,x,。),(1.12)S,(xl([8」3.1)。(1.13)W,,x。),,…,x,n):141996w,(xl,…,x。)~S,(,,…,x。)。/、w,0,l,.”,JJ`lw..t·xlx`,…wxj...tx,x`,…jl(x,…x。)`’(wJ1…x,lx,+,…x)(xl…x.`lwjxl’xjlx+jl.”xJ=1_wjxl”`xlx1`’`xw,…x,lx,,“`。]l,l(.10)(1.13)a~1。,ao,1.4(1.9)Pa,ao,(y,,…,1)-1(`+y,),`“(Xl,,1+,{t“{`(1.14)、、~_、aB__,,“,(xl,`”,’。)`;`,xj、、、.S,(x,,S,(x,,,J(1.15)a1,1a,S`a1-;x,)x,(x,,XS,(xl,…,xj~\l~\{}~!】1\x]/\,j、.、.S,(x,,…,x)。(1.14),x(:,’`’,x。)w,(xl,…,x.)-w,S,(x,,…,x,),…,x。)w,s,(x,w,x’w,x:~lw`,a1,w,(x,,:…,x。)x,w,x’w,x(;,…,x.)x(,,…,x,),(,,…,x,)x,,x;J=1wxj’:[8]1.1w.3,。]=l:,(x,,,x)x,(1.5),w,(x,,…,x,)1,:()15:,,,_’,(1.16):dxltl,,J12,2,,dxdxz2,nld,dB,l(1.17)w,。zw,dBm:1,1=,,n22,=`2,w,x,l。lx`1,。B。,B:(w。x;w,x,,w,nxZWZx,’,wox。lw,,x。,woBx,)O(1.18)。,B:B(x,,…,x.)(x.+“w,wlx.,…,w,x,n,wl,))(1.19)2。;.5(1.19)(,:,…,,,,),,,J~l-B(xl,…,x.x[.+(w。xltw,x。+。wZx.+…+。x。,w._,x。)〕+〔w,x(;+ZJ+…+x。1)x,(wl+:+…+w,l)]+(x,+xZ+…+X。,“w·,(1.11)。w,:w:l(.11);:,+c:w;B,…,x。+c。~dxlt,tw,BdB,dBx,+`,Bw,`,””?,`,“““x(1,X,·。gard(x,+。)gardx,,。。,l(.11)。]IJ~l,(l.18)(1.19),B;,,B.1(wojl6(l8),,(y,,…,。,,。)E,:,wl。)“+(w:、)2+…+(w)’Ix,。;,n,。)2+(w,B)2O1996“”B:wBZZw,,xoB+c=(1.20)`ww2。x。wxj,+x+1).(l.2。):Zwox。+V4wx4wZw1—X。,。`)BZ:B;,(x。`),。2「sj(1.1)“”:w,(x,,…,x。)x,(j1,…,m);,,,“”。,,,。,“”,“”,,;“”,,“”;,fjx,,x,。,:2.1(m)mw,(j1,2,…,m):,:0,1]m~〔o,l〕,(x,,…,x)~w,(,,…,x,。):w·1):w,(x,,…,。)-·2):w,x(,,·3):w,(x,,,x,)(j1,,x,)(j1,,m);,m),,。“”,[8」3.1·2):·2’)x,)S,x(,,…,x。))S,(x,,…,x,)。。2.IBx(1,…,x,。)x,,,,。2.2B(1;a1,,…,x。):,1.u~l)x,,、2.1,a1,B/{“’、1。l,”’,J,njZjJ、JjjB(x,,…,x,)。:(Ix)3“”,,fl,…,,+:,…,f,n,1Pm.,:3.1(m)mw,(j1,…,m):W,:[o,1]’~。,1」,(:,…,x。)~w,(x,,…,x):·1):w,x(,,…,x。)~1;,…,m);·2):w,(x,,…,x。)(j~1,.3:w,(xl,’“,x,)j~1,…,P)x,,w,(x,,…,x,)(jP+1,…,m)x,。3.1,([8〕3.1:·2,)):·2)`·2’’)P:1Pm,ix)x,,s`x(,,…,x。)s,(xl,…,x。),1i,J(Ps,(1,…,x。))s,(xl,…,x.),P+li,7m:1《iP,+1,m,,,。3·l“(1,。)+…+X,+(X1+…+X:),`。`、_j`,、,,ax,}x,1jPP+1jm:·2.,、、1iPP+1(jmp1imwJ,n,,+wxj,J~l,=P+l1Jm1]P,p+1,mw,+w,….|11.、、XXZ、w,(,,…,,,)·3“).,xj),1jp,:,(,,…,,,,x,,x,+,,…,,,),,(,,…,,,,:,,,,…,)P+1Jm,JP+1,:()WebeFechner;WebeFechner,。,,,(4.5)。[10].(l).().(n).().(l).().(vI).().(v).().().().(、.,9(2),1995.().,9(3),1995,..:,1994HongxingLi,VineentC.Yen.FuzzySetsandFuzzyDeeisionMaking,CRVPress,1995,..:,1993,..:,1994_,.Fuzyz(l).(),1995,189196..:,1993..:,1959..:,1979ǐIJ11J,.lJes.Jesl」110nJJLLJU1nO6JrrL.JlweILLLweìLFLLFlorida,[1lj[12〕[13)31(2),[14〕[15〕[16〕FactorSaPcesandMathematiealFrameofKnowledgeRePresentation(XI)StruCtureofBslanCeFunctionsandWeberFechner`5CharacteristicsLiHongxing(r.ofth.,BeijingNormalUniversiyt,100875)AbstraCtThispaper15theninthofaseriesofpapersofdiseussingindetailfaetorspaeesandknowledgerePresentarionbasedonfaetorsPaees.ThisPaPerfoeusesonstruetureofbal-aneefunetionsonvariableweights.Andfromakindofvariableweightsthemultifaeto-rialfunetionwithWeberFeehner,5eharaeteristies15gained.Key,odrsFaetorspaees;Knowledgerepresentation;Balaneefunetions;Weber-Feehner`5law:()WebeFechner;WebeFechner,。,,,(4.5)。[10].(l).().(n).().(l).().(vI).().(v).().().().(、.,9(2),1995.().,9(3),1995,..:,1994HongxingLi,VineentC.Yen.FuzzySetsandFuzzyDeeisionMaking,CRVPress,1995,..:,1993,..:,1994_,.Fuzyz(l).(),1995,189196..:,1993..:,1959..:,1979ǐIJ11J,.lJes.Jesl」110nJJLLJU1nO6JrrL.JlweILLLweìLFLLFlorida,[1lj[12〕[13)31(2),[14〕[15〕[16〕FactorSaPcesandMathematiealFrameofKnowledgeRePresentation(XI)StruCtureofBslanCeFunctionsandWeberFechner`5CharacteristicsLiHongxing(r.ofth.,BeijingNormalUniversiyt,100875)AbstraCtThispaper15theninthofaseriesofpapersofdiseussingindetailfaetorspaeesandknowledgerePresentarionbasedonfaetorsPaees.ThisPaPerfoeusesonstruetureofbal-aneefunetionsonvariableweights.Andfromakindofvariableweightsthemultifaeto-rialfunetionwithWeberFeehner,5eharaeteristies15gained.Key,odrsFaetorspaees;Knowledgerepresentation;Balaneefunetions;Weber-Feehner`5law