Fuzzy Sets and Fuzzy Logic: Theory and Applications

Description

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 to the present, this book not only details the theoretical advances in these areas, but considers a broad variety of applications of fuzzy sets and fuzzy logic as well. Theoretical aspects of fuzzy set theory and fuzzy logic are covered in Part I of the text, including: basic types of fuzzy sets; connections between fuzzy sets and crisp sets; the various aggregation operations of fuzzy sets; fuzzy numbers and arithmetic operations on fuzzy numbers; fuzzy relations and the study of fuzzy relation equations. Part II is devoted to applications of fuzzy set theory and fuzzy logic, including: various methods for constructing membership functions of fuzzy sets; the use of fuzzy logic for approximate reasoning in expert systems; fuzzy systems and controllers; fuzzy databases; fuzzy decision making; and engineering applications. For everyone interested in an introduction to fuzzy set theory and fuzzy logic. FUZZY SETS AND FUZZY LOGIC: THEORY AND APPLICATIONS......Page 1 Title Page......Page 2 Copyright Page......Page 3 Dedication......Page 5 Contents......Page 6 Foreword......Page 12 Preface......Page 14 1.1 Introduction......Page 17 1.2 Crisp Sets: An Overview......Page 21 1.3 Fuzzy Sets: Basic Types......Page 27 1.4 Fuzzy Sets: Basic Concepts......Page 35 1.5 Characteristics and Significance of the Paradigm Shift......Page 46 Notes......Page 48 Exercises......Page 49 2.1 Additional Properties of α-Cuts......Page 51 2.2 Representations of Fuzzy Sets......Page 55 2.3 Extension Principle for Fuzzy Sets......Page 60 Notes......Page 64 Exercises......Page 65 3.1 Types of Operations......Page 66 3.2 Fuzzy Complements......Page 67 3.3 Fuzzy Intersections: t-Norms......Page 77 3.4 Fuzzy Unions: t-Conorms......Page 92 3.5 Combinations of Operations......Page 99 3.6 Aggregation Operations......Page 104 Notes......Page 110 Exercises......Page 111 4.1 Fuzzy Numbers......Page 113 4.3 Arithmetic Operations on Intervals......Page 118 4.4 Arithmetic Operations on Fuzzy Numbers......Page 121 4.5 Lattice of Fuzzy Numbers......Page 125 4.6 Fuzzy Equations......Page 130 Exercises......Page 133 5.1 Crisp and Fuzzy Relations......Page 135 5.2 Projections and Cylindric Extensions......Page 138 5.3 Binary Fuzzy Relations......Page 140 5.4 Binary Relations on a Single Set......Page 144 5.5 Fuzzy Equivalence Relations......Page 148 5.6 Fuzzy Compatibility Relations......Page 151 5.7 Fuzzy Ordering Relations......Page 153 5.8 Fuzzy Morphisms......Page 157 5.9 Sup-i Compositions of Fuzzy Relations......Page 160 5.10 Inf-ω i Compositions of Fuzzy Relations......Page 162 Exercises......Page 165 6.1 General Discussion......Page 169 6.2 Problem Partitioning......Page 170 6.3 Solution Method......Page 172 6.3 Fuzzy Relation Equations Based on Sup-i Compositions......Page 178 6.5 Fuzzy Relation Equations Based on Inf-ω i Compositions......Page 180 6.6 Approximate Solutions......Page 182 6.7 The Use of Neural Networks......Page 187 Notes......Page 189 Exercises......Page 191 7.1 Fuzzy Measures......Page 193 7.2 Evidence Theory......Page 196 7.3 Possibility Theory......Page 203 7.4 Fuzzy Sets and Possibility Theory......Page 214 7.5 Possibility Theory versus Probability Theory......Page 216 Notes......Page 224 Exercises......Page 225 8.1 Classical Logic: An Overview......Page 228 8.2 Multivalued Logics......Page 233 8.3 Fuzzy Propositions......Page 236 8.4 Fuzzy Quantifiers......Page 241 8.5 Linguistic Hedges......Page 245 8.6 Inference from Conditional Fuzzy Propositions......Page 247 8.7 Inference from Conditional and Qualified Propositions......Page 252 8.8 Inference from Quantified Propositions......Page 255 Exercises......Page 258 9.1 Information and Uncertainty......Page 261 9.2 Nonspecificity of Crisp Sets......Page 263 9.3 Nonspecificity of Fuzzy Sets......Page 266 9.4 Fuzziness of Fuzzy Sets......Page 270 9.5 Uncertainty in Evidence Theory......Page 274 9.6 Summary of Uncertainty Measures......Page 283 9.7 Principles of Uncertainty......Page 285 Notes......Page 293 Exercises......Page 294 10.1 General Discussion......Page 296 10.2 Methods of Construction: An Overview......Page 297 10.3 Direct Methods with One Expert......Page 298 10.4 Direct Methods with Multiple Experts......Page 299 10.5 Indirect Methods with One Expert......Page 303 10.6 Indirect Methods with Multiple Experts......Page 304 10.7 Constructions from Sample Data......Page 306 Notes......Page 316 Exercises......Page 317 11.1 Fuzzy Expert Systems: An Overview......Page 318 11.2 Fuzzy Implications......Page 320 11.3 Selection of Fuzzy Implications......Page 328 11.4 Multiconditional Approximate Reasoning......Page 333 11.5 The Role of Fuzzy Relation Equations......Page 337 11.6 Interval-Valued Approximate Reasoning......Page 339 Exercises......Page 341 12.1 General Discussion......Page 343 12.2 Fuzzy Controllers: An Overview......Page 346 12.3 Fuzzy Controllers: An Example......Page 355 12.4 Fuzzy Systems and Neural Networks......Page 360 12.5 Fuzzy Neural Networks......Page 363 12.6 Fuzzy Automata......Page 365 12.7 Fuzzy Dynamic Systems......Page 369 Notes......Page 370 Exercises......Page 372 13.1 Introduction......Page 373 13.2 Fuzzy Clustering......Page 374 13.3 Fuzzy Pattern Recognition......Page 381 13.4 Fuzzy Image Processing......Page 390 Notes......Page 393 Exercises......Page 394 14.1 General Discussion......Page 395 14.2 Fuzzy Databases......Page 397 14.3 Fuzzy Information Retrieval......Page 401 Exercises......Page 404 15.1 General Discussion......Page 406 15.2 Individual Decision Making......Page 407 15.3 Multiperson Decision Making......Page 411 15.4 Multicriteria Decision Making......Page 415 15.5 Multistage Decision Making......Page 417 15.6 Fuzzy Ranking Methods......Page 421 15.7 Fuzzy Linear Programming......Page 424 Notes......Page 431 Exercises......Page 432 16.1 Introduction......Page 434 16.2 Civil Engineering......Page 435 16.3 Mechanical Engineering......Page 442 16.4 Industrial Engineering......Page 448 16.5 Computer Engineering......Page 452 16.6 Reliability......Page 455 Notes......Page 456 Exercises......Page 457 17.2 Medicine......Page 459 17.3 Economics......Page 466 17.4 Fuzzy Systems and Genetic Algortihms......Page 468 17.5 Fuzzy Regression......Page 470 17.6 Interpersonal Communication......Page 475 17.7 Other Applications......Page 479 Notes......Page 481 Exercises......Page 482 Appendix A. Artificial Neural Networks: An Overview......Page 483 Appendix B. Genetic Algorithms: An Overview......Page 492 Appendix C. Fuzzy Sets versus Rough Sets......Page 497 D.1 The Proof of Theorem 3.7 (Sec. 3.2, p. 59)......Page 500 D.2 Proof of Theorem 3.13 (Sec. 3.3, p. 75)......Page 501 D.3 Proof of Theorem 3.28 (Sec. 3.6, p. 96)......Page 502 Appendix E. Glossary of Key Concepts......Page 503 General Symbols......Page 506 Special Symbols......Page 508 Bibliography......Page 510 Bibliographical Index......Page 564 Name Index......Page 568 A-B......Page 579 C......Page 580 D-E......Page 581 F......Page 582 G-H-I......Page 583 J-K-L-M......Page 584 N-O......Page 585 P......Page 586 Q-R......Page 587 S......Page 588 T-U-V......Page 589 W-X-Y-Z......Page 590