Fuzzy Logic with Engineering Applications, Third Edition

INTRODUCTION......Page 23
THE CASE FOR IMPRECISION......Page 24
A HISTORICAL PERSPECTIVE......Page 25
THE UTILITY OF FUZZY SYSTEMS......Page 28
LIMITATIONS OF FUZZY SYSTEMS......Page 30
THE ILLUSION: IGNORING UNCERTAINTY AND ACCURACY......Page 32
UNCERTAINTY AND INFORMATION......Page 35
FUZZY SETS AND MEMBERSHIP......Page 36
CHANCE VERSUS FUZZINESS......Page 38
SETS AS POINTS IN HYPERCUBES......Page 40
REFERENCES......Page 42
PROBLEMS......Page 43
CLASSICAL SETS AND FUZZY SETS......Page 47
CLASSICAL SETS......Page 48
Operations on Classical Sets......Page 50
Properties of Classical (Crisp) Sets......Page 51
Mapping of Classical Sets to Functions......Page 54
FUZZY SETS......Page 56
Fuzzy Set Operations......Page 57
Properties of Fuzzy Sets......Page 59
Alternative Fuzzy Set Operations......Page 62
SUMMARY......Page 63
PROBLEMS......Page 64
CLASSICAL RELATIONS AND FUZZY RELATIONS......Page 70
CRISP RELATIONS......Page 71
Cardinality of Crisp Relations......Page 73
Properties of Crisp Relations......Page 74
Composition......Page 75
FUZZY RELATIONS......Page 76
Fuzzy Cartesian Product and Composition......Page 77
TOLERANCE AND EQUIVALENCE RELATIONS......Page 84
Crisp Equivalence Relation......Page 85
Crisp Tolerance Relation......Page 86
FUZZY TOLERANCE AND EQUIVALENCE RELATIONS......Page 87
VALUE ASSIGNMENTS......Page 90
Cosine Amplitude......Page 91
Other Similarity Methods......Page 93
SUMMARY......Page 94
PROBLEMS General Relations......Page 95
Similarity......Page 106
Other Composition Operations......Page 109
PROPERTIES OF MEMBERSHIP FUNCTIONS, FUZZIFICATION, AND DEFUZZIFICATION......Page 111
FEATURES OF THE MEMBERSHIP FUNCTION......Page 112
VARIOUS FORMS......Page 114
FUZZIFICATION......Page 115
DEFUZZIFICATION TO CRISP SETS......Page 117
-CUTS FOR FUZZY RELATIONS......Page 119
DEFUZZIFICATION TO SCALARS......Page 120
SUMMARY......Page 132
REFERENCES......Page 133
PROBLEMS......Page 134
PART I LOGIC......Page 139
Classical Logic......Page 140
Proof......Page 146
Fuzzy Logic......Page 153
Approximate Reasoning......Page 156
Other Forms of the Implication Operation......Page 160
PART II FUZZY SYSTEMS......Page 161
Natural Language......Page 162
Linguistic Hedges......Page 164
Fuzzy (Rule-Based) Systems......Page 167
Graphical Techniques of Inference......Page 170
SUMMARY......Page 181
REFERENCES......Page 183
PROBLEMS......Page 184
DEVELOPMENT OF MEMBERSHIP FUNCTIONS......Page 196
Intuition......Page 197
Inference......Page 198
Rank Ordering......Page 200
Neural Networks......Page 201
Genetic Algorithms......Page 211
Inductive Reasoning......Page 221
REFERENCES......Page 228
PROBLEMS......Page 229
AUTOMATED METHODS FOR FUZZY SYSTEMS......Page 233
DEFINITIONS......Page 234
BATCH LEAST SQUARES ALGORITHM......Page 237
RECURSIVE LEAST SQUARES ALGORITHM......Page 241
GRADIENT METHOD......Page 244
CLUSTERING METHOD......Page 249
LEARNING FROM EXAMPLES......Page 251
MODIFIED LEARNING FROM EXAMPLES......Page 255
REFERENCES......Page 264
PROBLEMS......Page 265
FUZZY SYSTEMS SIMULATION......Page 267
FUZZY RELATIONAL EQUATIONS......Page 272
NONLINEAR SIMULATION USING FUZZY SYSTEMS......Page 273
FUZZY ASSOCIATIVE MEMORIES (FAMS)......Page 277
SUMMARY......Page 286
REFERENCES......Page 287
PROBLEMS......Page 288
DECISION MAKING WITH FUZZY INFORMATION......Page 298
FUZZY SYNTHETIC EVALUATION......Page 300
FUZZY ORDERING......Page 302
NONTRANSITIVE RANKING......Page 305
PREFERENCE AND CONSENSUS......Page 307
MULTIOBJECTIVE DECISION MAKING......Page 311
FUZZY BAYESIAN DECISION METHOD......Page 316
DECISION MAKING UNDER FUZZY STATES AND FUZZY ACTIONS......Page 326
SUMMARY......Page 339
REFERENCES......Page 340
PROBLEMS Ordering and Synthetic Evaluation......Page 341
Nontransitive Ranking......Page 342
Fuzzy Preference and Consensus......Page 344
Multiobjective Decision Making......Page 346
Bayesian Decision Making......Page 349
FUZZY CLASSIFICATION......Page 354
CLASSIFICATION BY EQUIVALENCE RELATIONS Crisp Relations......Page 355
Fuzzy Relations......Page 357
CLUSTER ANALYSIS......Page 361
-MEANS CLUSTERING......Page 362
-MEANS (HCM)......Page 363
-MEANS (FCM)......Page 371
-Means Algorithm......Page 374
CLASSIFICATION METRIC......Page 379
-PARTITION......Page 382
SIMILARITY RELATIONS FROM CLUSTERING......Page 383
REFERENCES......Page 384
PROBLEMS Exercises for Equivalence Classificatio......Page 385
-Means......Page 386
Exercises for Classificatio Metric and Similarity......Page 389
FUZZY PATTERN RECOGNITION......Page 391
FEATURE ANALYSIS......Page 392
SINGLE-SAMPLE IDENTIFICATION......Page 393
MULTIFEATURE PATTERN RECOGNITION......Page 400
IMAGE PROCESSING......Page 412
SUMMARY......Page 420
REFERENCES......Page 421
Exercises for Multifeature Pattern Recognition......Page 422
Exercises for Image Processing......Page 429
EXTENSION PRINCIPLE......Page 430
Crisp Functions, Mapping, and Relations......Page 431
Fuzzy Transform (Mapping)......Page 433
Practical Considerations......Page 435
FUZZY ARITHMETIC......Page 440
INTERVAL ANALYSIS IN ARITHMETIC......Page 442
APPROXIMATE METHODS OF EXTENSION......Page 444
Vertex Method......Page 445
DSW Algorithm......Page 448
Restricted DSW Algorithm......Page 450
Comparisons......Page 451
SUMMARY......Page 454
PROBLEMS......Page 455
FUZZY CONTROL SYSTEMS......Page 459
CONTROL SYSTEM DESIGN PROBLEM......Page 461
Control (Decision) Surface......Page 462
Simple Fuzzy Logic Controllers......Page 463
EXAMPLES OF FUZZY CONTROL SYSTEM DESIGN......Page 464
Aircraft Landing Control Problem......Page 468
Classical Feedback Control......Page 475
Fuzzy Control......Page 479
FUZZY STATISTICAL PROCESS CONTROL......Page 486
Measurement Data – Traditional SPC......Page 488
Attribute Data – Traditional SPC......Page 494
INDUSTRIAL APPLICATIONS......Page 500
SUMMARY......Page 501
REFERENCES......Page 504
PROBLEMS......Page 506
FUZZY OPTIMIZATION......Page 523
One-Dimensional Optimization......Page 524
Concept Variables and Causal Relations......Page 530
Fuzzy Cognitive Maps......Page 532
AGENT-BASED MODELS......Page 542
SUMMARY......Page 546
REFERENCES......Page 547
PROBLEMS Fuzzy Optimization......Page 548
Fuzzy Cognitive Mapping......Page 550
Fuzzy Agent-Based Models......Page 551
MONOTONE MEASURES: BELIEF, PLAUSIBILITY, PROBABILITY, AND POSSIBILITY......Page 552
MONOTONE MEASURES......Page 553
BELIEF AND PLAUSIBILITY......Page 554
EVIDENCE THEORY......Page 559
PROBABILITY MEASURES......Page 562
POSSIBILITY AND NECESSITY MEASURES......Page 564
POSSIBILITY DISTRIBUTIONS AS FUZZY SETS......Page 571
POSSIBILITY DISTRIBUTIONS DERIVED FROM EMPIRICAL INTERVALS......Page 573
Deriving Possibility Distributions from Overlapping Intervals......Page 574
Redistributing Weight from Nonconsonant to Consonant Intervals......Page 576
Comparison of Possibility Theory and Probability Theory......Page 590
SUMMARY......Page 591
REFERENCES......Page 593
PROBLEMS......Page 594