基于T_S模型的模糊神经网络_孙增圻.pdf

b¿vÐÐ(1– SÐñ) 18/26``1997M»37 Journal of Tsinghua University (Sci & Tech)»3ù»76j80:`基于T-S模型的模糊神经网络孙增圻,　徐红兵b¿vÐ9Ø SÐÐ/Œ";Æ?/ŒÐ"dSE×ÄLi,Ø100084``là°ù: 1996-07-04``»BT€:3, 1943M3,qÓ`K`一种基于Takagi-Sugeno模型的模糊神经网络由前件网络和后件网络两部分组成前件网络用来匹配模糊规则的前件,它相当于每条规则的适用度后件网络用来实现模糊规则的后件总的输出为各模糊规则后件的加权和,加权系数为各条规则的适用度所提出的模糊神经网络具有局部逼近功能,且具有神经网络和模糊逻辑两者的优点它既可以容易地表示模糊和定性的知识,又具有较好的学习能力给出了调整规则后件参数及前件隶属度函数参数的学习算法,举例说明了它的逼近性能1oM`模糊逻辑; 神经网络; T-S模型; 函数逼近s Ë|`TP 18``*Ü©Ž µi›9ØasƒTi%a¸p? ï 0¹Ðqb¾´*Ü©9„BP©#CMAC©B",'É9^LCV{Æž{¥dLŸ˜bñ„BP©B",²û^ª- Œ©,ÐØEû^YVµQ.¥ZE;ñ„CMAC©B",û‹¿ †/Í©Žb/ëYVBñdLŸf”˜¥ è0 Ÿªü¾©Ž¥Ÿ?b4　举　例!µÂ/=»dLŸf”f (x1, x2)= sin(Px1)cos(Px2) ,Ïx 1‰[ - 1,1] , x2‰[ - 1,1]bC¨ëó¥´*Ü©Ž ŸLC¾dLŸ˜b!|{Æx1„x2 (s¹3ñ´©),ñÌ‹¿VNžP¥3ñ´Ôýë,'m1= m2=3b î‹f”¥™¹.™sƒ,1Øœ¥^ªq•”p jl#-q•”cisi„Risib¹´*Ü©ŽÉ›Þ,³1Ê|Þ"'bƒ Ú¿$x1= $x2= 0.1¥Wï (|Ä,¨ë¥³TÉ› ؂9Ø,¤ž441F{Æ{¥"'” b 樃t"'” m1îU¥´*Ü©Ž(Ïn= 2, m1= m2= 3, m= 9, r= 1)É›Þ,Øœ©Ž•”bm4(a)îU¹Ðª´*Ü©ŽîLC¥{Æ{˜¥Ø»m™b¹1 ,m4(b)Ï]Hó³9ؤž¥Ø»m™b V A´*Ü©Žó z¥/ÍrTb¹|´*Ü©ŽÐBP©ŽÉ›1 ,m4(c)AUBP©ŽM]"'"/¾f”É›/Í¥²Tb V[ A,´*Ü©Žó1BP©Žz¥²T:´*Ü©¥/͵¹0.492 6,7BP©Ž¥/͵¹0. 697 2b(a)´*Ü©Ž{¥Ø»m™(b)`³T9زT( c)`BP©Ž{m4`Ø»m™5　结束语´*Ü©ŽÙ–9^ †/Í©Ž,Œñ^¿v´"d˜y ë¥,©ŽÏ¥òñ²Ä#” (µüA¥þ Øil,yNƒt•”¥´79ä9¯,©:`¿T-S˜¥´*Ü©Ž V[ô "d¥´çŸ¥©M ŸF[’ç,–ª 樍¥ÐØE V[“ yl ûž1p¥{Æ{1",ƒ^´*Ü©Ž1-ë†B¥*Ü©Ž¥ªÄb]H®¿ñ µ*Ü©Ž¥²,y7•”¥Ð„Øœ1 ¸^,ƒ^ñ1†B¥´† "d¥ªÄb¿T-S˜¥´*Ü©Ž VV6B˜ŸªMñ¥˜1",{Ñwëf” V Aî^sLŸÄÑÜ르/Íb¿ƒ"¥ س, VúùÊ4p kjl¥´,V7 VEçJÆ‚¬¥ †´ivv4Úl û¥Î,ƒBÄ¿LH eÅ^­¹×1¥b•` I`Ó`D1 Takagi T, Sugeno M. Fuzzy identification of systemsand its application to modeling and control. IEEETrans on Systems, Man, and Cybernetics, 1985, 15( 1) : 116j1322 Lin C T, Lee C S G. Neural-network-based fuzzylogic control and decision systems. IEEE Trans onComputers, 1991, 12: 1320j13363 Lee C C. Fuzzy logic in control systems: fuzzy logiccontroller, Partú&û. IEEE Trans on Systems,Man and Cybernetics, 1990, 20: 404j4354¬½ê,ä9¯,f–.BÕ´CM AC*Ü©Ž.1îÄÐ, 1995,21(3): 288j2945ä9¯,¬½ê.BÕ Ë»CMAC¥´*Ü©Ž# eÅÏ¥‹¨.b¿vÐÐ, 1996, 36( 5) :17j23Fuzzy-neural network basedon T-S modelSunZengqi, Xu HongbinDepartment of Computer Science and Technology,Tsinghua U niversity; State Key Laboratory ofIntelligent Technology and Systems,Beijing 100084Abstract:`The network based on Takagi-Sugeno model iscomprised of two parts: premise network and consequentnetwork. The premise network is to match thepremise of afuzzy rule. The output of the premise network correspondsto the fitness value of a fuzzy rule. The consequent networkcomputes the consequence of a fuzzy rule. The total outputis equal to the weighting sum with weighting coefficientsbeing equal to the fitness value of fuzzy rules. The proposednetwork has the ability of local mapping, which showsadvantages of both neural network and fuzzy logic. Thenetwork can express the fuzzy and qualitative knowledgeeasily. It also has good learning capacity. The learningalgirithms for tuning consequent parameters andmembership parameters in premise are derived. An exampleis given to show the approximation abilities of the fuzzy-neural network.Key words:`fuzzy logic; neural network; Takagi-Sugeno(T-S) model; function approximation80b¿vÐÐ(1– SÐñ) 1997, 37(3)。