## Fuzzy set theory--and its applicationsSince its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request. |

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### Contents

Introduction to Fuzzy Sets | 1 |

Fuzzy Mathematics | 9 |

Extensions | 23 |

Copyright | |

12 other sections not shown

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### Common terms and phrases

a-level aggregation algebraic algorithm alternative applications of fuzzy approach areas assignment assume Bezdek chapter clustering compute concepts considered constraints crisp criteria criterion decision maker defined definition degree of membership denotes described determined Dubois and Prade empirical example expert systems extension principle formal fuzzy clustering fuzzy control fuzzy event fuzzy function fuzzy graph fuzzy logic fuzzy numbers fuzzy relation fuzzy set decision fuzzy set theory given goal grades of membership heuristic iA(x inference integral interpreted intersection interval knowledge linear programming linguistic variable logic programming mathematical matrix max-min maximize membership function min-operator necessary support objective function operations research optimal parameters partition pattern recognition possibility distribution possibility theory probability probability theory problem proposition PRUF relationship representing respect rule of inference rules schedule shown in figure solution space statements structure symmetric true truth tables truth values uncertainty Yager young Zadeh Zimmermann