What Is Fuzzy Logic?

More documents

Recommendations

Info

2 Tutorial How does it work? Reasoning in fuzzy logicisjustamatterofgeneralizing the familiar yes-no (Boolean) logic. If you give true the numerical value of 1 and false the numerical value of 0, this value indicates that fuzzy logic also permits in-between values like 0.2 and 0.7453. For instance: Q: Is Saturday a weekend day? A: 1 (yes, or true) Q: Is Tuesday a weekend day? A: 0 (no, or false) Q: Is Friday a weekend day? A: 0.8 (for the most part yes, but not completely) Q: Is Sunday a weekend day? A: 0.95 (yes, but not quite as much as Saturday). The following plot on the left shows the truth values for weekend-ness if you areforcedtorespondwithanabsoluteyesornoresponse.Ontheright,isa plot that shows the truth value for weekend-ness if you are allowed to respond with fuzzy in-between values. 1.0 1.0 weekend-ness weekend-ness 0.0 0.0 Thursday Friday Saturday Sunday Monday Thursday Friday Saturday Sunday Monday Days of the weekend two-valued membership Days of the weekend multivalued membership Technically, the representation on the right is from the domain of multivalued logic (or multivalent logic). If you ask the question “Is X a member of set A?” the answer might be yes, no, or any one of a thousand intermediate values in between. Thus, X might have partial membership in A. Multivalued logic stands in direct contrast to the more familiar concept of two-valued (or bivalent yes-no) logic. To return to the example, now consider a continuous scale time plot of weekend-ness shown in the following plots. 2-6
Foundations of Fuzzy Logic By making the plot continuous, you are definingthedegreetowhichanygiven instant belongs in the weekend rather than an entire day. In the plot on the left, notice that at midnight on Friday, just as the second hand sweeps past 12, the weekend-ness truth value jumps discontinuously from 0 to 1. This is one way to define the weekend, and while it may be useful to an accountant, it may not really connect with your own real-world experience of weekend-ness. Theplotontherightshowsasmoothlyvarying curve that accounts for the fact that all of Friday, and, to a small degree, parts of Thursday, partake of the quality of weekend-ness and thus deserve partial membership in the fuzzy set of weekend moments. The curve that defines the weekend-ness of any instant in time is a function that maps the input space (time of the week) to the output space (weekend-ness). Specifically it is known as a membership function. See “Membership Functions” on page 3-3 for a more detailed discussion. As another example of fuzzy sets, consider the question of seasons. What season is it right now? In the northern hemisphere, summer officially begins at the exact moment in the earth’s orbit when the North Pole is pointed most directly toward the sun. It occurs exactly once a year, in late June. Using the astronomical definitions for the season, you get sharp boundaries as shown on the left in the figurethatfollows.Butwhatyou experience as the seasons vary more or less continuously as shown on the right in the following figure (in temperate northern hemisphere climates). 1.0 sprin g summer fall winter 1.0 sprin g summer fall winter degree of membership degree of membership 0.0 0.0 March March March June September December March June September December Time of the year Time of the year Membership Functions A membership function (MF) is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1. The input space is sometimes referred to as the universe of discourse, afancynameforasimpleconcept. 2-7
Page 1 and 2: Fuzzy Logic Toolbox 2 User’s Guid
Page 3: Revision History January 1995 First
Page 6 and 7: Overview of Fuzzy Inference Process
Page 8 and 9: Simulink Environment ..............
Page 10 and 11: x Contents
Page 12 and 13: 1 Getting Started Product Overview
Page 14 and 15: 1 Getting Started If you just want
Page 16 and 17: 1 Getting Started Another basic con
Page 18 and 19: 1 Getting Started Input Space (all
Page 20 and 21: 1 Getting Started do a fine job wit
Page 22 and 23: 1 Getting Started An Introductory E
Page 24 and 25: 1 Getting Started See how the formu
Page 26 and 27: 1 Getting Started tip=(0.15)*servRa
Page 28 and 29: 1 Getting Started 0.25 0.2 tip 0.15
Page 30 and 31: 1 Getting Started or perhaps rewrit
Page 32 and 33: 2 Tutorial Overview The point of fu
Page 34 and 35: 2 Tutorial Foundations of Fuzzy Log
Page 38 and 39: 2 Tutorial One of the most commonly
Page 40 and 41: 2 Tutorial A fuzzy set is an extens
Page 42 and 43: 2 Tutorial Polynomial based curves
Page 44 and 45: 2 Tutorial A B min(A,B) A B max(A,B
Page 46 and 47: 2 Tutorial the fuzzy sets to be com
Page 48 and 49: 2 Tutorial if temperature is cold t
Page 50 and 51: 2 Tutorial Fuzzy Inference Systems
Page 52 and 53: 2 Tutorial Information flows from l
Page 54 and 55: 2 Tutorial selects the maximum of t
Page 56 and 57: 2 Tutorial In the following diagram
Page 58 and 59: 2 Tutorial 1. if and then Interpret
Page 60 and 61: 2 Tutorial Customization Oneofthepr
Page 62 and 63: 2 Tutorial adaptive neural fuzzy in
Page 64 and 65: 2 Tutorial Getting Started We’ll
Page 66 and 67: 2 Tutorial Name of the system. Chan
Page 68 and 69: 2 Tutorial 8 Select File > Export >
Page 70 and 71: 2 Tutorial Editor shares some featu
Page 72 and 73: 2 Tutorial can first use the mouse
Page 74 and 75: 2 Tutorial d Verify that 3 is selec
Page 76 and 77: 2 Tutorial 5 In the FIS Variables a
Page 78 and 79: 2 Tutorial Now that the variables h
Page 80 and 81: 2 Tutorial one of the variable qual
Page 82 and 83: 2 Tutorial A literal interpretation
Page 84 and 85: 2 Tutorial Notice that under food,
Page 86 and 87:
2 Tutorial Upon opening the Surface
Page 88 and 89:
2 Tutorial Building Fuzzy Inference
Page 90 and 91:
2 Tutorial Specifying Custom Member
Page 92 and 93:
2 Tutorial 3 In the FIS Editor, sel
Page 94 and 95:
2 Tutorial Using the custmf1 exampl
Page 96 and 97:
2 Tutorial 6 To add custom membersh
Page 98 and 99:
2 Tutorial In the toolbox, the AND
Page 100 and 101:
2 Tutorial 1 In the lower-left pane
Page 102 and 103:
2 Tutorial Working from the Command
Page 104 and 105:
2 Tutorial The structure.field synt
Page 106 and 107:
2 Tutorial After closing any open M
Page 108 and 109:
2 Tutorial 25 20 tip 15 10 5 10 8 6
Page 110 and 111:
2 Tutorial a.output(1).mf(2).type='
Page 112 and 113:
2 Tutorial All the information for
Page 114 and 115:
2 Tutorial 44. 2 The list of comman
Page 116 and 117:
2 Tutorial Working in Simulink Envi
Page 118 and 119:
2 Tutorial 2 1.8 1.6 1.4 1.2 1 0.8
Page 120 and 121:
2 Tutorial 0.8 0.6 0.4 0.2 valve 0
Page 122 and 123:
2 Tutorial If you stop the simulati
Page 124 and 125:
2 Tutorial FIS. This automatic mode
Page 126 and 127:
2 Tutorial Type slcp attheMATLABpro
Page 128 and 129:
2 Tutorial As the figure shows, the
Page 130 and 131:
2 Tutorial The final output of the
Page 132 and 133:
2 Tutorial the Sugeno-type represen
Page 134 and 135:
2 Tutorial and the membership funct
Page 136 and 137:
2 Tutorial anfis and the ANFIS Edit
Page 138 and 139:
2 Tutorial alone or in combination
Page 140 and 141:
2 Tutorial Constraints of anfis anf
Page 142 and 143:
2 Tutorial You can also load Testin
Page 144 and 145:
2 Tutorial Validating the Trained F
Page 146 and 147:
2 Tutorial The training data appear
Page 148 and 149:
2 Tutorial 1 Choose Grid partition,
Page 150 and 151:
2 Tutorial Viewing Your FIS Structu
Page 152 and 153:
2 Tutorial The plot shows the check
Page 154 and 155:
2 Tutorial • Select the Checking
Page 156 and 157:
2 Tutorial In this case, the checki
Page 158 and 159:
2 Tutorial anfis from the Command L
Page 160 and 161:
2 Tutorial data values. You use the
Page 162 and 163:
2 Tutorial subplot(2,2,4) plotmf(fi
Page 164 and 165:
2 Tutorial Thedifferencebetweentheo
Page 166 and 167:
2 Tutorial As a result, the trainin
Page 168 and 169:
2 Tutorial Output FIS Structure for
Page 170 and 171:
2 Tutorial Output FIS Structure for
Page 172 and 173:
2 Tutorial right location within a
Page 174 and 175:
2 Tutorial Here, the variable cente
Page 176 and 177:
2 Tutorial Finally, plot the two cl
Page 178 and 179:
2 Tutorial The genfis2 function bui
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
Page 190 and 191:
2 Tutorial information on the clust
Page 192 and 193:
2 Tutorial Saving the Cluster Cente
Page 194 and 195:
2 Tutorial The fis.c file contains
Page 196 and 197:
2 Tutorial This command saves the i
Page 198 and 199:
2 Tutorial 'lcclnk' is not recogniz
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 224 and 225:
fcm Purpose Syntax Description Fuzz
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
Page 274 and 275:
uleedit Purpose Syntax Description
Page 276 and 277:
uleview Purpose Syntax Rule viewer
Page 278 and 279:
setfis Purpose Syntax Description S
Page 280 and 281:
sffis Purpose Syntax Description Fu
Page 282 and 283:
showfis 24. average 25. generous 26
Page 284 and 285:
showrule 1. (service==poor) | (food
Page 286 and 287:
sigmf See Also dsigmf, gaussmf, gau
Page 288 and 289:
subclust Purpose Syntax Description
Page 290 and 291:
subclust Examples [C,S] = subclust(
Page 292 and 293:
surfview If you want to create a sm
Page 294 and 295:
trapmf Purpose Syntax Description T
Page 296 and 297:
trimf Purpose Syntax Description Tr
Page 298 and 299:
writefis Purpose Syntax Description
Page 300 and 301:
zmf See Also dsigmf, gaussmf, gauss
Page 302 and 303:
5 Block Reference Controllers Fuzzy
Page 304 and 305:
5 Block Reference Membership Functi
Page 306 and 307:
Diff. Sigmoidal MF Purpose Descript
Page 308 and 309:
Fuzzy Logic Controller with Rulevie
Page 310 and 311:
Gaussian2 MF Purpose Description Co
Page 312 and 313:
Pi-shaped MF Purpose Description Se
Page 314 and 315:
Probabilistic Rule Agg Purpose Desc
Page 316 and 317:
S-shaped MF Purpose Description See
Page 318 and 319:
Trapezoidal MF Purpose Description
Page 320 and 321:
Z-shaped MF Purpose Description See
Page 322 and 323:
A Examples Introductory Examples
Page 324 and 325:
B Bibliography [1] Bezdec, J.C., Pa
Page 326 and 327:
B Bibliography [22] Zadeh, L.A.,
Page 328 and 329:
Glossary fuzzy c-means clustering A
Page 330 and 331:
Glossary Glossary-4
Page 332 and 333:
Index H hybrid method 2-121 I if-th
show all

What Is Fuzzy Logic?

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?