1、 6c 201 6c 6.1 f 6.1.1 f f gaussmf T y=gaussmf(x,sig c) f Vr T222)cx(e)c,;x(f= c, x 1M sig Vr T b 6-1 x=0:0.1:10; y=gaussmf(x,2 5); plot(x,y) xlabel(gaussmf, P=2 5) Tm 6-1b 0 2 4 6 8 1000.20.40.60.81gaussmf, P=2 5m 6-1 6.1.2 H f f gauss2mf T y = gauss2mf(x,sig1 c1 sig2 c2) sig1ac1asig2ac2 7 1 Vr T 6
2、-2 x = (0:0.1:10); y1 = gauss2mf(x, 2 4 1 8); y2 = gauss2mf(x, 2 5 1 7); y3 = gauss2mf(x, 2 6 1 6); y4 = gauss2mf(x, 2 7 1 5); y5 = gauss2mf(x, 2 8 1 4); MATLAB6.0 m 202 plot(x, y1 y2 y3 y4 y5); set(gcf, name, gauss2mf, numbertitle, off); Tm 6-2b 6.1.3 y B f f gbellmf T y = gbellmf(x,params) B f G L
3、f Vr Tb2|acx|11)c,b,a;x(f+= xM lS bY c wL= M params BsY a b c_ b 6-3 x=0:0.1:10; y=gbellmf(x,2 4 6); plot(x,y) xlabel(gbellmf, P=2 4 6) Tm 6-3b 0 2 4 6 8 1000.20.40.60.810 2 4 6 8 1000.20.40.60.81gbellmf, P=2 4 6m 6-2 m 6-3 6.1.4 sigmoid f F f f dsigmf T y = dsigmf(x,a1 c1 a2 c2) sigmoid f / T)cx(ae
4、11)c,a;x(f+= x M a,c b dsigmf P a1 c1 a2 c2i O sigmoid f )c,a;x(f)c,a;x(f222111 caca2211b 6-4 x=0:0.1:10; y=dsigmf(x,5 2 5 7); plot(x,y) Tm 6-4 6c 203 0 2 4 6 8 1000.20.40.60.81m 6-4 6.1.5 Y f 9 f evalmf T y = evalmf(x, mfParams, mfType) evalmf V9 i f x M l mfType Q4B f mfParams N f M T FX7y1l f eva
5、lmf VTy V9 3 i f b 6-5 x=0:0.1:10; mfparams = 2 4 6; mftype = gbellmf; y=evalmf(x,mfparams,mftype); plot(x,y) xlabel(gbellmf, P=2 4 6) Tm 6-5b 0 2 4 6 8 1000.20.40.60.81gbellmf, P=2 4 6m 6-5 6.1.6 y j f f primf T y = pimf(x,a b c d) _ x f 1M lf _ x )9 a,b,c,d % f a dsY wL/P . b csY wLP .b 6-6 MATLAB
6、6.0 m 204 x=0:0.1:10; y=pimf(x,1 4 5 10); plot(x,y) xlabel(pimf, P=1 4 5 10) Tm 6-6b 6.1.7 YV sigmoid f / f f psigmf T y = psigmf(x,a1 c1 a2 c2) sigmoid f / T)cx(ae11)c,a;x(f+= x M a,c b psigmf P a1 c1 a2 c2i O sigmoid f )c,a;x(f)c,a;x(f222111 caca2211b 6-7 x=0:0.1:10; y=psigmf(x,2 3 -5 8); plot(x,y
7、) xlabel(psigmf, P=2 3 -5 8) Tm 6-7b 0 2 4 6 8 1000.20.40.60.81pimf, P=1 4 5 100 2 4 6 8 1000.20.40.60.81psigmf, P=2 3 -5 8m 6-6 m 6-7 6.1.8 y Sigmoid f f sigmf T y = sigmf(x,a c) )cx(ae11)c,a;x(f+= l_ x a c b 6-8 x=0:0.1:10; y=sigmf(x,2 4); plot(x,y) xlabel(sigmf, P=2 4) Tm 6-8b 6c 205 0 1 2 3 4 5
8、6 7 8 9 1000.10.20.30.40.50.60.70.80.91sigmf, P=2 4m 6-8 6-9 x = (0:0.2:10); y1= sigmf(x,-1 5); y2= sigmf(x,-3 5); y3= sigmf(x,4 5); y4= sigmf(x,8 5); subplot(2,1,1),plot(x,y1 y2 y3 y4); y1= sigmf(x,5 2); y2= sigmf(x,5 4); y3= sigmf(x,5 6); y4= sigmf(x,5 8); subplot(2,1,2),plot(x,y1 y2 y3 y4); Tm 6-
9、9b 0 2 4 6 8 1000.510 2 4 6 8 1000.51m 6-9 6.1.9 y S f f smf T y = smf(x,a b) % xM a b wL| sb 6-10 x=0:0.1:10; y=smf(x,1 8); plot(x,y) Tm 6-10b MATLAB6.0 m 206 0 2 4 6 8 1000.20.40.60.81smf, P=1 8m 6-10 6-11 x = 0:0.1:10; subplot(3,1,1);plot(x,smf(x,2 8); subplot(3,1,2);plot(x,smf(x,4 6); subplot(3,
10、1,3);plot(x,smf(x,6 4); Tm 6-11b 0 1 2 3 4 5 6 7 8 9 1000.510 1 2 3 4 5 6 7 8 9 1000.510 1 2 3 4 5 6 7 8 9 1000.51m 6-11 6.1.10 y 0 f f trapmf T y = trapmf(x,a b c d) 0 f Vr T=xd0dxc,cdxdcxb,1bxa,abaxax,0)d,c,b,a;x(f f(x;a,b,c,d) = max(min( )0),cdxd,1,abaxl_ x wL a,b,c,d a d0/P . b c0 P 6c 207 .b 6-
11、12 x=0:0.1:10; y=trapmf(x,1 5 7 8); plot(x,y) xlabel(trapmf, P=1 5 7 8) Tm 6-12b 6-13 x = (0:0.1:10); y1= trapmf(x,2 3 7 9); y2 = trapmf(x,3 4 6 8); y3= trapmf(x,4 5 5 7); y4= trapmf(x,5 6 4 6); plot(x,y1 y2 y3 y4); Tm 6-13b 0 1 2 3 4 5 6 7 8 9 1000.10.20.30.40.50.60.70.80.91trapmf, P=1 5 7 8 0 2 4
12、6 8 1000.20.40.60.81m 6-12 m 6-13 6.1.11 y f f trimf T y = trimf(x,params) y = trimf(x,a b c) f Vr T=xc0cxb,bcxcbxa,abaxax,0),c,b,a;x(f f(x;a,b,c,) = max(min( )0),bcxc,abaxl_ x wL a,b,c a c /P b 1 p a cb , 3 f 9BdB XBldB f 5 P trapmff b 6-14 MATLAB6.0 m 208 x=0:0.1:10; y=trimf(x,3 6 8); plot(x,y) xl
13、abel(trimf, P=3 6 8) Tm 6-14b 0 1 2 3 4 5 6 7 8 9 1000.10.20.30.40.50.60.70.80.91trimf, P=3 6 8m 6-14 6-15 x = (0:0.2:10); y1= trimf(x,3 4 5); y2 = trimf(x,2 4 7 ); y3= trimf(x,1 4 9); subplot(2,1,1),plot(x,y1 y2 y3 ); y1= trimf(x,2 3 5); y2 = trimf(x,3 4 7); y3= trimf(x,4 5 9); subplot(2,1,2),plot(
14、x,y1 y2 y3 ); Tm 6-15b 0 1 2 3 4 5 6 7 8 9 1000.20.40.60.810 1 2 3 4 5 6 7 8 9 1000.20.40.60.81m 6-15 6.1.12 y Z f f zmf T y = zmf(x,a b) % x1M a b wLb 6-16 x=0:0.1:10; y=zmf(x,3 7); plot(x,y) 6c 209 xlabel(zmf, P=3 7) Tm 6-16b 6-17 x = 0:0.1:10; subplot(3,1,1);plot(x,zmf(x,2 8); subplot(3,1,2);plot
15、(x,zmf(x,4 6); subplot(3,1,3);plot(x,zmf(x,6 4); Tm 6-17b 0 2 4 6 8 1000.20.40.60.81zmf, P=3 70 2 4 6 8 1000.510 2 4 6 8 1000.510 2 4 6 8 1000.51m 6-16 m 6-17 6.1.13 f W f mf2mf T outParams = mf2mf(inParams,inType,outType) Nf “| i =y f 6B inParamsF1 f inType F1 f 31 outType: F1 “S f 31 b 6-18 x=0:0.
16、1:5; mfp1 = 1 2 3; mfp2 = mf2mf(mfp1,gbellmf,trimf); plot(x,gbellmf(x,mfp1),x,trimf(x,mfp2) Tm 6-18b 6.1.14 FISI f fuzzy T fuzzy %l FISI fuzzy(fismat) % P fuzzy(tipper)/m FISI b I i w “dA U F I TbN FZL I iK 2Z T “db Z m3 g ZZ mA U a W ?5) b iBM PZ -M N H M Z b iBM 0 1 2 3 4 500.20.40.60.81m 6-18 MAT
17、LAB6.0 m 210 f I ?5I ?5I b m 6-19 FISI Fu 7M u 7i i“db cFile New mamdani FIS u 7 mamdani “d New Sugeno FIS u 7 Sugeno“d Open from disk VH u 7 .fisq“d Save to disk i -“dH B .fisq Save to disk as Z T i -“dH Open from workspace VT bW FISM B“d Save to workspace i“dT bW - FISM Save to workspace as i“dT b
18、W FISM Close windows 1 GUI cEdit Add input 9F 6B -“d Add output 9F 6B -“d Remove variable “B M Undo -KM cView Edit MFs f I Edit rules ?5I Edit anfis Sugeno“dI View rules ?54 View surface w 4 b T T M cV ? cAnd methodB T4 minaprod Custom cOr methodB T4 maxaprobor q Custom cImplication methodB T4 minap
19、rod Custom N Sugeno “d Vb 6c 211 cAggregation methodB T4 maxasumaprobor CustombN Sugeno “d Vb cDefuzzification method Mamdaniw B T4 centroidE abisector sE amom (Kv E asom Kv KlE alom Kv KvE Customb Sugenow wtaver F ( wtsum F W4b 6.1.15 f I f mfedit T mfedit(a) mfedit(a) mfedit mfedit(a) 3B f I F_i%q
20、 a.fis FIS f b m mfedit(tank)Z Tu 7 f I i tank.fisi% f b mfedit(a) FIS TB MATLABT bWM abMfedit V FIS f I m 6-20 ANFISI GUI B Fu 7M1 GUI au 7 i“db File FISI File ?Mb cEdit Add MF -M 9F f Add custom MF -M 9F f Remove current MF “ - f Remove all MFS “ -M f Undo -KMb cView Edit FIS properties FISI MATLA
21、B6.0 m 212 Edit rules ?5I View rules ?54 View surface w 4 b 6.2 w FIS 6.2.1 P ZEV 3 FIS f genfis1 T fismat = genfis1(data) fismat = genfis1(data,numMFs,inmftype, outmftype) genfis1 anfis 3B Sugeno T SHq FIS S f bgenfis1(data,numMFs,inmftype, outmftype) P sZEV “ 3B FISb Data “KB V UB VU b NumMFs B_ U
22、S B M1 f b TFX P M1M f * P numMFsB bInmftype B31 F M1 f b outmftype B31 F M1 f 6-19 data = rand(10,1) 10*rand(10,1)-5 rand(10,1); numMFs = 3 7; mfType = str2mat(pimf,trimf); fismat = genfis1(data,numMFs,mfType); x,mf = plotmf(fismat,input,1); subplot(2,1,1), plot(x,mf); xlabel(input 1 (pimf); x,mf =
23、 plotmf(fismat,input,2); subplot(2,1,2), plot(x,mf); xlabel(input 2 (trimf); Tm 6-21b 0 0.2 0.4 0.6 0.8 100.51input 1 (pimf)-4 -3 -2 -1 0 1 2 3 4 500.51input 2 (trimf)m 6-21 6c 213 6.2.2 PhE ZEV 3 FIS f genfis2 T fismat = genfis2(Xin,Xout,radii) fismat = genfis2(Xin,Xout,radii,xBounds) fismat = genf
24、is2(Xin,Xout,radii,xBounds,options) Xin B BcB Xout B BcB randi B_ B B TS L B Z8 = xBounds B 2N V | Xin Xout B Z8 = options B V_ E 8b 6-20 fismat = genfis2(Xin,Xout,0.5) PNf KlM b 0.5TSb fismat = genfis2(Xin,Xout,0.5 0.25 0.3) LF 3bL ! Xin a Xout B * 0.5 0.25 Xin BTS 0.3 Xout TSb fismat = genfis2(Xin
25、,Xout,0.5,-10 -5 0; 10 5 20) | Xin Xout ?S 0 1 uW ) b L! Xin a XoutB * XinB V -10 +101 MXin= V -5 +51 M Xout V 0 201 Mb 6.2.3 3B FIS w f gensurf T gensurf(fis) % P - B 3 w “d (fis) w gensurf(fis,inputs,output) % PsY_ input S output B B 3Bmb gensurf(fis,inputs,output,grids) % X Ba Y =aa = readfis(tip
26、per); gensurf(a) Tm 6-22b MATLAB6.0 m 214 m 6-22 6.2.4 | mamdan FIS Sugeno FIS f mam2sug T sug_fis=mam2sug(mam_fis) f |B mamdani FIS A mam_fisB sugeno sug_fisbR sugeno “d f bt mamdani“dq f E b -q Mb 6.2.5 w 9 f evalfis T output= evalfis(input,fismat) output= evalfis(input,fismat, numPts) output, IRR
27、, ORR, ARR= evalfis(input,fismat) output, IRR, ORR, ARR= evalfis(input,fismat, numPts) input B B T B MN N M * evalfis P input BTB _ i OM outputR ML B B_ i O L M fismat19 B FIS numPtsB VM V U S =“ t 9 f T PNM P 101 8b Evalfis / Outputvl ML M V U - LVU FIS M b evalfis VM input B_ H9 t VM IRRYV f 9 M T
28、 Bvl numRulesN numRules ?5H N M b ORRYV f 9 M T BvlnumPtsnumRulesL numRules ?5H L M N BF numRules B =F 6c 215 numRules = GQ wb ARR numPts)“ numPtsL BM H f P fismat w“dS inout 9 _ outputb 6-22 fismat = readfis(tipper); out = evalfis(2 1; 4 9,fismat) T out = 7.0169 19.6810 6.2.6 c ( f fcm T center,U,o
29、bj_fcn = fcm(data,cluster_n) “ c ( ZE data1 “ B“ cluster_n v 1 center US U s f Obj_fcnV “Sf fcm(data,cluster_n,options) P VM options e b T5 / !A U options(1)s U 8 2.0 options(2)KvQ 8 100 options(3)Kl T5 8 1e-5 option(4)VA U 8 1b T iB NaNt P 8 rKvQ H “Sf Q lKl T5 H V b 6-23 data = rand(100, 2); center,U,obj_fcn = fcm(data, 2); plot(data(:,1), data(:,2),o); maxU = max(U); index1 = find(U(1,:) = maxU); index2 = find(U(2, :) = maxU); line(data(index1,1), data(index1, 2), linestyle
