Fuzzy Sets and Fuzzy Logic: Theory and Applications

Description

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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.

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Book Info :

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Provides the reader with comprehensive coverage of theoretical foundations of fuzzy set theory and fuzzy logic, as well as a broad overview of the increasingly important applications of these novel areas of mathematics. DLC: Fuzzy sets.

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Table of Contents :

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Foreword Preface 1 From Classical (Crisp) Sets to Fuzzy Sets: A Grand Paradigm Shift 1 2 Fuzzy Sets Versus Crisp Sets 35 3 Operations on Fuzzy Sets 50 4 Fuzzy Arithmetic 97 5 Fuzzy Relations 119 6 Fuzzy Relation Equations 153 7 Possibility Theory 177 8 Fuzzy Logic 212 9 Uncertainty-Based Information 245 10 Constructing Fuzzy Sets and Operations on Fuzzy Sets 280 11 Approximate Reasoning 302 12 Fuzzy Systems 327 13 Pattern Recognition 357 14 Fuzzy Databases and Information Retrieval Systems 379 15 Fuzzy Decision Making 390 16 Engineering Applications 418 17 Miscellaneous Applications 443 Appendix A. Neural Networks: An Overview 467 Appendix B. Genetic Algorithms: An Overview 476 Appendix C. Rough Sets Versus Fuzzy Sets 481 Appendix D. Proofs of Some Mathematical Theorems 484 Appendix E. Glossary of Key Concepts 487 Appendix F. Glossary of Symbols 490 Bibliography 494 Bibliographical Index 548 Name Index 552 Subject Index 563

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