The first edition of Fuzzy Logic with Engineering Applications (1995) was the first classroom text for undergraduates in the field. Now updated for the second time, this new edition features the latest advances in the field including material on expansion of the MLFE method using genetic algorithms, cognitive mapping, fuzzy agent-based models and total uncertainty. Redundant or obsolete topics have been removed, resulting in a more concise yet inclusive text that will ensure the book retains its broad appeal at the forefront of the literature.
Fuzzy Logic with Engineering Applications, 3rd Edition is oriented mainly towards methods and techniques. Every chapter has been revised, featuring new illustrations and examples throughout. Supporting MATLAB code is downloadable at www.wileyeurope.com/go/fuzzylogic. This will benefit student learning in all basic operations, the generation of membership functions, and the specialized applications in the latter chapters of the book, providing an invaluable tool for students as well as for self-study by practicing engineers.
Table of Contents:
About the Author xiii
Preface to the Third Edition xv
1 Introduction 1
The Case for Imprecision 2
A Historical Perspective 3
The Utility of Fuzzy Systems 6
Limitations of Fuzzy Systems 8
The Illusion: Ignoring Uncertainty and Accuracy 10
Uncertainty and Information 13
The Unknown 14
Fuzzy Sets and Membership 14
Chance Versus Fuzziness 16
Sets as Points in Hypercubes 18
Summary 20
References 20
Problems 21
2 Classical Sets and Fuzzy Sets 25
Classical Sets 26
Operations on Classical Sets 28
Properties of Classical (Crisp) Sets 29
Mapping of Classical Sets to Functions 32
Fuzzy Sets 34
Fuzzy Set Operations 35
Properties of Fuzzy Sets 37
Alternative Fuzzy Set Operations 40
Summary 41
References 42
Problems 42
3 Classical Relations and Fuzzy Relations 48
Cartesian Product 49
Crisp Relations 49
Cardinality of Crisp Relations 51
Operations on Crisp Relations 52
Properties of Crisp Relations 52
Composition 53
Fuzzy Relations 54
Cardinality of Fuzzy Relations 55
Operations on Fuzzy Relations 55
Properties of Fuzzy Relations 55
Fuzzy Cartesian Product and Composition 55
Tolerance and Equivalence Relations 62
Crisp Equivalence Relation 63
Crisp Tolerance Relation 64
Fuzzy Tolerance and Equivalence Relations 65
Value Assignments 68
Cosine Amplitude 69
Max–Min Method 71
Other Similarity Methods 71
Other Forms of the Composition Operation 72
Summary 72
References 73
Problems 73
4 Properties of Membership Functions, Fuzzification, and Defuzzification 89
Features of the Membership Function 90
Various Forms 92
Fuzzification 93
Defuzzification to Crisp Sets 95
λ-Cuts for Fuzzy Relations 97
Defuzzification to Scalars 98
Summary 110
References 111
Problems 112
5 Logic and Fuzzy Systems 117
Part I Logic 117
Classical Logic 118
Proof 124
Fuzzy Logic 131
Approximate Reasoning 134
Other Forms of the Implication Operation 138
Part II Fuzzy Systems 139
Natural Language 140
Linguistic Hedges 142
Fuzzy (Rule-Based) Systems 145
Graphical Techniques of Inference 148
Summary 159
References 161
Problems 162
6 Development of Membership Functions 174
Membership Value Assignments 175
Intuition 175
Inference 176
Rank Ordering 178
Neural Networks 179
Genetic Algorithms 189
Inductive Reasoning 199
Summary 206
References 206
Problems 207
7 Automated Methods for Fuzzy Systems 211
Definitions 212
Batch Least Squares Algorithm 215
Recursive Least Squares Algorithm 219
Gradient Method 222
Clustering Method 227
Learning From Examples 229
Modified Learning From Examples 233
Summary 242
References 242
Problems 243
8 Fuzzy Systems Simulation 245
Fuzzy Relational Equations 250
Nonlinear Simulation Using Fuzzy Systems 251
Fuzzy Associative Memories (FAMS) 255
Summary 264
References 265
Problems 266
9 Decision Making with Fuzzy Information 276
Fuzzy Synthetic Evaluation 278
Fuzzy Ordering 280
Nontransitive Ranking 283
Preference and Consensus 285
Multiobjective Decision Making 289
Fuzzy Bayesian Decision Method 294
Decision Making Under Fuzzy States and Fuzzy Actions 304
Summary 317
References 318
Problems 319
10 Fuzzy Classification 332
Classification by Equivalence Relations 333
Crisp Relations 333
Fuzzy Relations 335
Cluster Analysis 339
Cluster Validity 340
c-Means Clustering 340
Hard c-Means (HCM) 341
Fuzzy c-Means (FCM) 349
Fuzzy c-Means Algorithm 352
Classification Metric 357
Hardening the Fuzzy c-Partition 360
Similarity Relations from Clustering 361
Summary 362
References 362
Problems 363
11 Fuzzy Pattern Recognition 369
Feature Analysis 370
Partitions of the Feature Space 371
Single-Sample Identification 371
Multifeature Pattern Recognition 378
Image Processing 390
Summary 398
References 399
Problems 400
12 Fuzzy Arithmetic and the Extension Principle 408
Extension Principle 408
Crisp Functions, Mapping, and Relations 409
Functions of Fuzzy Sets – Extension Principle 411
Fuzzy Transform (Mapping) 411
Practical Considerations 413
Fuzzy Arithmetic 418
Interval Analysis in Arithmetic 420
Approximate Methods of Extension 422
Vertex Method 423
DSW Algorithm 426
Restricted DSW Algorithm 428
Comparisons 429
Summary 432
References 433
Problems 433
13 Fuzzy Control Systems 437
Control System Design Problem 439
Control (Decision) Surface 440
Assumptions in a Fuzzy Control System Design 441
Simple Fuzzy Logic Controllers 441
Examples of Fuzzy Control System Design 442
Aircraft Landing Control Problem 446
Fuzzy Engineering Process Control 453
Classical Feedback Control 453
Fuzzy Control 457
Fuzzy Statistical Process Control 464
Measurement Data – Traditional SPC 466
Attribute Data – Traditional SPC 472
Industrial Applications 478
Summary 479
References 482
Problems 484
14 Miscellaneous Topics 501
Fuzzy Optimization 501
One-Dimensional Optimization 502
Fuzzy Cognitive Mapping 508
Concept Variables and Causal Relations 508
Fuzzy Cognitive Maps 510
Agent-Based Models 520
Summary 524
References 525
Problems 526
15 Monotone Measures: Belief, Plausibility, Probability, and Possibility 530
Monotone Measures 531
Belief and Plausibility 532
Evidence Theory 537
Probability Measures 540
Possibility and Necessity Measures 542
Possibility Distributions as Fuzzy Sets 549
Possibility Distributions Derived from Empirical Intervals 551
Deriving Possibility Distributions from Overlapping Intervals 552
Redistributing Weight from Nonconsonant to Consonant Intervals 554
Comparison of Possibility Theory and Probability Theory 568
Summary 569
References 571
Problems 572
Index 579
