Fuzzy Logic with Engineering Applications

About the Author xi Preface to the Fourth Edition xiii 1 Introduction 1 The Case for Imprecision 2 A Historical Perspective 4 The Utility of Fuzzy Systems 7 Limitations of Fuzzy Systems 9 The Illusion: Ignoring Uncertainty and Accuracy 11 Uncertainty and Information 13 Fuzzy Sets and Membership 14 Chance versus Fuzziness 17 Intuition of Uncertainty: Fuzzy versus Probability 19 Sets as Points in Hypercubes 21 Summary 23 References 23 Problems 24 2 Classical Sets and Fuzzy Sets 27 Classical Sets 28 Fuzzy Sets 36 Summary 45 References 46 Problems 46 3 Classical Relations and Fuzzy Relations 51 Cartesian Product 52 Crisp Relations 53 Fuzzy Relations 58 Tolerance and Equivalence Relations 67 Fuzzy Tolerance and Equivalence Relations 70 Value Assignments 72 Other Forms of the Composition Operation 76 Summary 77 References 77 Problems 77 4 Properties of Membership Functions, Fuzzification, and Defuzzification 84 Features of the Membership Function 85 Various Forms 87 Fuzzification 88 Defuzzification to Crisp Sets 90 lambda-Cuts for Fuzzy Relations 92 Defuzzification to Scalars 93 Summary 102 References 103 Problems 104 5 Logic and Fuzzy Systems 107 Part I: Logic 107 Classical Logic 108 Fuzzy Logic 122 Part II: Fuzzy Systems 132 Summary 151 References 153 Problems 154 6 Historical Methods of Developing Membership Functions 163 Membership Value Assignments 164 Intuition 164 Inference 165 Rank Ordering 167 Neural Networks 168 Genetic Algorithms 179 Inductive Reasoning 188 Summary 195 References 196 Problems 197 7 Automated Methods for Fuzzy Systems 201 Definitions 202 Batch Least Squares Algorithm 205 Recursive Least Squares Algorithm 210 Gradient Method 213 Clustering Method 218 Learning from Examples 221 Modified Learning from Examples 224 Summary 233 References 235 Problems 235 8 Fuzzy Systems Simulation 237 Fuzzy Relational Equations 242 Nonlinear Simulation Using Fuzzy Systems 243 Fuzzy Associative Memories (FAMs) 246 Summary 257 References 258 Problems 259 9 Decision Making with Fuzzy Information 265 Fuzzy Synthetic Evaluation 267 Fuzzy Ordering 269 Nontransitive Ranking 272 Preference and Consensus 275 Multiobjective Decision Making 279 Fuzzy Bayesian Decision Method 285 Decision Making under Fuzzy States and Fuzzy Actions 295 Summary 309 References 310 Problems 311 10 Fuzzy Classification and Pattern Recognition 323 Fuzzy Classification 324 Classification by Equivalence Relations 324 Cluster Analysis 332 Cluster Validity 332 c-Means Clustering 333 Hard c-Means (HCM) 333 Fuzzy c-Means (FCM) 343 Classification Metric 351 Hardening the Fuzzy c-Partition 354 Similarity Relations from Clustering 356 Fuzzy Pattern Recognition 357 Single-Sample Identification 357 Multifeature Pattern Recognition 365 Summary 378 References 379 Problems 380 11 Fuzzy Control Systems 388 Control System Design Problem 390 Examples of Fuzzy Control System Design 393 Fuzzy Engineering Process Control 404 Fuzzy Statistical Process Control 417 Industrial Applications 431 Summary 434 References 437 Problems 438 12 Applications of Fuzzy Systems Using Miscellaneous Models 455 Fuzzy Optimization 455 Fuzzy Cognitive Mapping 462 Agent-Based Models 477 Fuzzy Arithmetic and the Extension Principle 481 Fuzzy Algebra 487 Data Fusion 491 Summary 498 References 498 Problems 500 13 Monotone Measures: Belief, Plausibility, Probability, and Possibility 505 Monotone Measures 506 Belief and Plausibility 507 Evidence Theory 512 Probability Measures 515 Possibility and Necessity Measures 517 Possibility Distributions as Fuzzy Sets 525 Possibility Distributions Derived from Empirical Intervals 528 Summary 548 References 549 Problems 550 Index 554