Fuzzy logic refers to a large subject dealing with a set of methods to characterize and quantify uncertainty in engineering systems that arise from ambiguity, imprecision, fuzziness, and lack of knowledge. Fuzzy logic is a reasoning system based on a foundation of fuzzy set theory, itself an extension of classical set theory, where set membership can be partial as opposed to all or none, as in the binary features of classical logic.
Fuzzy logic is a relatively new discipline in which major advances have been made over the last decade or so with regard to theory and applications. Following on from the successful first edition, this fully updated new edition is therefore very timely and much anticipated. Concentration on the topics of fuzzy logic combined with an abundance of worked examples, chapter problems and commercial case studies is designed to help motivate a mainstream engineering audience, and the book is further strengthened by the inclusion of an online solutions manual as well as dedicated software codes.
Senior undergraduate and postgraduate students in most engineering disciplines academics and practicing engineers, plus some working in economics, control theory, operational research etc, will all find this a valuable addition to their bookshelves.
Author(s): Timothy Ross
Edition: 2nd ed
Publisher: John Wiley
Year: 2004
Language: English
Pages: 652
City: Hoboken, NJ
Tags: Математика;Математическая логика;Нечеткая логика;
Contents......Page 9
About the Author......Page 15
Preface to the Second Edition......Page 17
1 Introduction......Page 25
The Case for Imprecision......Page 26
An Historical Perspective......Page 27
The Utility of Fuzzy Systems......Page 30
Limitations of Fuzzy Systems......Page 32
The Allusion: Statistics and Random Processes......Page 34
Uncertainty and Information......Page 36
Fuzzy Sets and Membership......Page 37
Chance versus Fuzziness......Page 39
Sets as Points in Hypercubes......Page 41
References......Page 43
Problems......Page 44
2 Classical Sets and Fuzzy Sets......Page 48
Classical Sets......Page 49
Operations on Classical Sets......Page 51
Properties of Classical (Crisp) Sets......Page 52
Mapping of Classical Sets to Functions......Page 56
Fuzzy Sets......Page 58
Fuzzy Set Operations......Page 59
Properties of Fuzzy Sets......Page 60
Noninteractive Fuzzy Sets......Page 65
Alternative Fuzzy Set Operations......Page 66
References......Page 67
Problems......Page 68
3 Classical Relations and Fuzzy Relations......Page 76
Crisp Relations......Page 77
Cardinality of Crisp Relations......Page 79
Properties of Crisp Relations......Page 80
Composition......Page 81
Fuzzy Relations......Page 82
Fuzzy Cartesian Product and Composition......Page 83
Crisp Equivalence Relation......Page 90
Crisp Tolerance Relation......Page 91
Fuzzy Tolerance and Equivalence Relations......Page 92
Value Assignments......Page 95
Cosine Amplitude......Page 96
Other Forms of the Composition Operation......Page 98
References......Page 99
General Relations......Page 100
Value Assignments and Similarity......Page 109
Other Composition Operations......Page 112
4 Properties of Membership Functions, Fuzzification, and Defuzzification......Page 114
Features of the Membership Function......Page 115
Various Forms......Page 117
Fuzzification......Page 118
Defuzzification to Crisp Sets......Page 120
λ-cuts for Fuzzy Relations......Page 122
Defuzzification to Scalars......Page 123
Summary......Page 136
References......Page 137
Problems......Page 138
Part I: Logic......Page 144
Classical Logic......Page 145
Tautologies......Page 150
Equivalence......Page 152
Exclusive Or and Exclusive Nor......Page 153
Logical Proofs......Page 154
Deductive Inferences......Page 156
Fuzzy Logic......Page 158
Approximate Reasoning......Page 161
Other Forms of the Implication Operation......Page 165
Part II: Fuzzy Systems......Page 166
Natural Language......Page 167
Linguistic Hedges......Page 169
Fuzzy (Rule-Based) Systems......Page 172
Graphical Techniques of Inference......Page 175
Summary......Page 186
References......Page 187
Problems......Page 189
6 Development of Membership Functions......Page 202
Intuition......Page 203
Inference......Page 204
Rank Ordering......Page 205
Neural Networks......Page 206
Genetic Algorithms......Page 217
Inductive Reasoning......Page 224
Summary......Page 230
References......Page 232
Problems......Page 233
7 Automated Methods for Fuzzy Systems......Page 236
Definitions......Page 237
Batch Least Squares Algorithm......Page 240
Recursive Least Squares Algorithm......Page 244
Gradient Method......Page 247
Clustering Method......Page 252
Learning From Example......Page 255
Modified Learning From Example......Page 258
Summary......Page 266
Problems......Page 267
8 Fuzzy Systems Simulation......Page 269
Fuzzy Relational Equations......Page 274
Nonlinear Simulation Using Fuzzy Systems......Page 275
Fuzzy Associative Memories (FAMs)......Page 278
Summary......Page 288
Problems......Page 289
9 Rule-base Reduction Methods......Page 298
New Methods......Page 299
Singular Value Decomposition......Page 300
Combs Method......Page 306
SVD and Combs Method Examples......Page 308
Summary......Page 327
Singular Value Decomposition......Page 328
Combs Method for Rapid Inference......Page 330
10 Decision Making with Fuzzy Information......Page 332
Fuzzy Synthetic Evaluation......Page 334
Fuzzy Ordering......Page 336
Nontransitive Ranking......Page 339
Preference and Consensus......Page 341
Multiobjective Decision Making......Page 344
Fuzzy Bayesian Decision Method......Page 350
Decision Making under Fuzzy States and Fuzzy Actions......Page 359
Summary......Page 373
Ordering and Synthetic Evaluation......Page 374
Nontransitive Ranking......Page 376
Fuzzy Preference and Consensus......Page 377
Multiobjective Decision Making......Page 379
Bayesian Decision Making......Page 381
Part I: Classification......Page 386
Crisp Relations......Page 387
Fuzzy Relations......Page 389
Cluster Analysis......Page 393
c-Means Clustering......Page 394
Hard c-Means (HCM)......Page 395
Fuzzy c-Means (FCM)......Page 403
Fuzzy c-Means Algorithm......Page 406
Classification Metric......Page 411
Hardening the Fuzzy c-Partition......Page 413
Similarity Relations from Clustering......Page 415
Part II: Pattern Recognition......Page 416
Partitions of the Feature Space......Page 417
Single-Sample Identification......Page 418
Multifeature Pattern Recognition......Page 424
Image Processing......Page 436
Syntactic Recognition......Page 444
Formal Grammar......Page 446
Fuzzy Grammar and Syntactic Recognition......Page 448
References......Page 453
Exercises for Equivalence Classification......Page 454
Exercises for Fuzzy c-Means......Page 455
Exercises for Classification Metric and Similarity......Page 458
Exercises for Fuzzy Vectors......Page 459
Exercises for Multifeature Pattern Recognition......Page 460
Exercises for Image Processing......Page 468
Extension Principle......Page 469
Crisp Functions, Mapping, and Relations......Page 470
Functions of Fuzzy Sets – Extension Principle......Page 471
Fuzzy Transform (Mapping)......Page 472
Practical Considerations......Page 474
Fuzzy Arithmetic......Page 479
Interval Analysis in Arithmetic......Page 481
Vertex Method......Page 483
DSW Algorithm......Page 486
Restricted DSW Algorithm......Page 489
Comparisons......Page 490
References......Page 493
Problems......Page 494
13 Fuzzy Control Systems......Page 500
Control System Design Problem......Page 502
Control (Decision) Surface......Page 503
Simple Fuzzy Logic Controllers......Page 504
Examples of Fuzzy Control System Design......Page 505
Aircraft Landing Control Problem......Page 509
Classical Feedback Control......Page 516
Classical PID Control......Page 518
Fuzzy Control......Page 520
Multi-input, Multi-output (MIMO) Control Systems......Page 524
Fuzzy Statistical Process Control......Page 528
Measurement Data – Traditional SPC......Page 529
Attribute Data – Traditional SPC......Page 534
Industrial Applications......Page 541
Summary......Page 542
References......Page 543
Problems......Page 545
Fuzzy Optimization......Page 561
One-dimensional Optimization......Page 562
Fuzzy Cognitive Mapping......Page 568
Fuzzy Cognitive Maps......Page 569
System Identification......Page 574
Fuzzy Linear Regression......Page 579
The Case of Nonfuzzy Data......Page 581
The Case of Fuzzy Data......Page 582
References......Page 591
Fuzzy Optimization......Page 592
System Identification......Page 593
Regression......Page 594
Cognitive Mapping......Page 595
15 Monotone Measures: Belief, Plausibility, Probability, and Possibility......Page 596
Monotone Measures......Page 597
Belief and Plausibility......Page 598
Evidence Theory......Page 602
Probability Measures......Page 606
Possibility and Necessity Measures......Page 607
Possibility Distributions as Fuzzy Sets......Page 614
Possibility Distributions Derived from Empirical Intervals......Page 616
Deriving Possibility Distributions from Overlapping Intervals......Page 617
Redistributing Weight from Nonconsonant to Consonant Intervals......Page 619
Comparison of Possibility Theory and Probability Theory......Page 624
Summary......Page 625
Problems......Page 627
Appendix A: Axiomatic Differences between Fuzzy Set Theory and Probability Theory......Page 634
Appendix B: Answers to Selected Problems......Page 638
Index of Examples and Problems by Discipline......Page 645
C......Page 647
E......Page 648
I......Page 649
N......Page 650
R......Page 651
X......Page 652
