What Is Fuzzy Logic?

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fcm Purpose Syntax Description <strong>Fuzzy</strong> c-means clustering [center,U,obj_fcn] = fcm(data,cluster_n) [center, U, obj_fcn] = fcm(data, cluster_n) applies the fuzzy c-means clustering method to a given data set. The input arguments of this function are • data: data set to be clustered; each row is a sample data point • cluster_n: number of clusters (greater than one) The output arguments of this function are • center: matrixoffinal cluster centers where each row provides the center coordinates • U: final fuzzy partition matrix (or membership function matrix) • obj_fcn: values of the objective function during iterations fcm(data,cluster_n,options) uses an additional argument variable, options, to control clustering parameters, introduce a stopping criteria, set the iteration information display, or both. • options(1): exponent for the partition matrix U (default: 2.0) • options(2): maximum number of iterations (default: 100) • options(3): minimum amount of improvement (default: 1e-5) • options(4): info display during iteration (default: 1) If any entry of options is NaN, the default value for that option is used instead. The clustering process stops when the maximum number of iterations is reached or when the objective function improvement between two consecutive iterations is less than the minimum amount of improvement specified. 4-18
fcm Examples 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','none',... 'marker','*','color','g'); line(data(index2,1),data(index2, 2),'linestyle','none',... 'marker', '*','color','r'); 4-19
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Fuzzy Logic Toolbox 2 User’s Guid
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Revision History January 1995 First
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Overview of Fuzzy Inference Process
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Simulink Environment ..............
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x Contents
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1 Getting Started Product Overview
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1 Getting Started If you just want
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1 Getting Started Another basic con
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1 Getting Started Input Space (all
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1 Getting Started do a fine job wit
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1 Getting Started An Introductory E
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1 Getting Started See how the formu
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1 Getting Started tip=(0.15)*servRa
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1 Getting Started 0.25 0.2 tip 0.15
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1 Getting Started or perhaps rewrit
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2 Tutorial Overview The point of fu
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2 Tutorial Foundations of Fuzzy Log
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2 Tutorial How does it work? Reason
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2 Tutorial One of the most commonly
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2 Tutorial A fuzzy set is an extens
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2 Tutorial Polynomial based curves
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2 Tutorial A B min(A,B) A B max(A,B
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2 Tutorial the fuzzy sets to be com
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2 Tutorial if temperature is cold t
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2 Tutorial Fuzzy Inference Systems
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2 Tutorial Information flows from l
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2 Tutorial selects the maximum of t
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2 Tutorial In the following diagram
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2 Tutorial 1. if and then Interpret
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2 Tutorial Customization Oneofthepr
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2 Tutorial adaptive neural fuzzy in
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2 Tutorial Getting Started We’ll
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2 Tutorial Name of the system. Chan
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2 Tutorial 8 Select File > Export >
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2 Tutorial Editor shares some featu
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2 Tutorial can first use the mouse
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2 Tutorial d Verify that 3 is selec
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2 Tutorial 5 In the FIS Variables a
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2 Tutorial Now that the variables h
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2 Tutorial one of the variable qual
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2 Tutorial A literal interpretation
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2 Tutorial Notice that under food,
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2 Tutorial Upon opening the Surface
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2 Tutorial Building Fuzzy Inference
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2 Tutorial Specifying Custom Member
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2 Tutorial 3 In the FIS Editor, sel
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2 Tutorial Using the custmf1 exampl
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2 Tutorial 6 To add custom membersh
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2 Tutorial In the toolbox, the AND
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2 Tutorial 1 In the lower-left pane
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2 Tutorial Working from the Command
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2 Tutorial The structure.field synt
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2 Tutorial After closing any open M
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2 Tutorial 25 20 tip 15 10 5 10 8 6
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2 Tutorial a.output(1).mf(2).type='
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2 Tutorial All the information for
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2 Tutorial 44. 2 The list of comman
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2 Tutorial Working in Simulink Envi
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2 Tutorial 2 1.8 1.6 1.4 1.2 1 0.8
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2 Tutorial 0.8 0.6 0.4 0.2 valve 0
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2 Tutorial If you stop the simulati
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2 Tutorial FIS. This automatic mode
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2 Tutorial Type slcp attheMATLABpro
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2 Tutorial As the figure shows, the
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2 Tutorial The final output of the
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2 Tutorial the Sugeno-type represen
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2 Tutorial and the membership funct
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2 Tutorial anfis and the ANFIS Edit
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2 Tutorial alone or in combination
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2 Tutorial Constraints of anfis anf
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2 Tutorial You can also load Testin
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2 Tutorial Validating the Trained F
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2 Tutorial The training data appear
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2 Tutorial 1 Choose Grid partition,
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2 Tutorial Viewing Your FIS Structu
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2 Tutorial The plot shows the check
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2 Tutorial • Select the Checking
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2 Tutorial In this case, the checki
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2 Tutorial anfis from the Command L
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2 Tutorial data values. You use the
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2 Tutorial subplot(2,2,4) plotmf(fi
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2 Tutorial Thedifferencebetweentheo
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2 Tutorial As a result, the trainin
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2 Tutorial Output FIS Structure for
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2 Tutorial Output FIS Structure for
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2 Tutorial right location within a
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Page 176 and 177: 2 Tutorial Finally, plot the two cl
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Page 180 and 181: 2 Tutorial fismat=genfis2(datin,dat
Page 182 and 183: 2 Tutorial At this point, you can u
Page 184 and 185: 2 Tutorial The next figure shows th
Page 186 and 187: 2 Tutorial you fit the fuzzy system
Page 188 and 189: 2 Tutorial Plot the checking error
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Page 192 and 193: 2 Tutorial Saving the Cluster Cente
Page 194 and 195: 2 Tutorial The fis.c file contains
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Page 200 and 201: 2 Tutorial 7 To verify that the fuz
Page 202 and 203: 3 Function Reference GUI Tools and
Page 204 and 205: 3 Function Reference FIS Data Struc
Page 206 and 207: 3 Function Reference Simulink Envir
Page 208 and 209: addmf Purpose Syntax Description Ad
Page 210 and 211: addrule Purpose Syntax Description
Page 212 and 213: anfis Purpose Syntax Description Tr
Page 214 and 215: anfis training data set. When you s
Page 216 and 217: anfisedit Purpose Syntax Descriptio
Page 218 and 219: defuzz Purpose Syntax Description D
Page 220 and 221: dsigmf See Also gaussmf, gauss2mf,
Page 222 and 223: evalfis • ORR: the result of eval
Page 226 and 227: findcluster Purpose Syntax Descript
Page 228 and 229: fuzarith Purpose Syntax Description
Page 230 and 231: fuzzy Purpose Syntax Open basic Fuz
Page 232 and 233: fuzzy Membership functions to invok
Page 234 and 235: gauss2mf See Also dsigmf, gauss2mf,
Page 236 and 237: gbellmf Purpose Syntax Description
Page 238 and 239: genfis1 The default number of membe
Page 240 and 241: genfis2 Purpose Syntax Description
Page 242 and 243: genfis2 Xin1 = 7*rand(50,1); Xin2 =
Page 244 and 245: genfis2 Example 3 The following exa
Page 246 and 247: genfis3 The input membership functi
Page 248 and 249: genfis3 Example 3 The following exa
Page 250 and 251: gensurf Example 1 a = readfis('tipp
Page 252 and 253: getfis 'inlabels' 'outlabels' 'inra
Page 254 and 255: getfis getfis(a,'input',1) Name = s
Page 256 and 257: mam2sug Purpose Syntax Description
Page 258 and 259: mf2mf 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3
Page 260 and 261: mfedit Selecttheiconforthevariableo
Page 262 and 263: newfis DefuzzMethod ans = [newsys]
Page 264 and 265: pimf Purpose Syntax Description Exa
Page 266 and 267: plotmf Purpose Syntax Description E
Page 268 and 269: psigmf Purpose Syntax Description B
Page 270 and 271: mmf Purpose Syntax Description Remo
Page 272 and 273: mvar Purpose Syntax Description Rem
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uleedit Purpose Syntax Description
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uleview Purpose Syntax Rule viewer
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setfis Purpose Syntax Description S
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sffis Purpose Syntax Description Fu
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showfis 24. average 25. generous 26
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showrule 1. (service==poor) | (food
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sigmf See Also dsigmf, gaussmf, gau
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subclust Purpose Syntax Description
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subclust Examples [C,S] = subclust(
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surfview If you want to create a sm
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trapmf Purpose Syntax Description T
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trimf Purpose Syntax Description Tr
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writefis Purpose Syntax Description
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zmf See Also dsigmf, gaussmf, gauss
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5 Block Reference Controllers Fuzzy
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5 Block Reference Membership Functi
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Diff. Sigmoidal MF Purpose Descript
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Fuzzy Logic Controller with Rulevie
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Gaussian2 MF Purpose Description Co
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Pi-shaped MF Purpose Description Se
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Probabilistic Rule Agg Purpose Desc
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S-shaped MF Purpose Description See
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Trapezoidal MF Purpose Description
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Z-shaped MF Purpose Description See
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A Examples Introductory Examples
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B Bibliography [1] Bezdec, J.C., Pa
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B Bibliography [22] Zadeh, L.A.,
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Glossary fuzzy c-means clustering A
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Glossary Glossary-4
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Index H hybrid method 2-121 I if-th
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What Is Fuzzy Logic?

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