## Fuzzy Sets and Fuzzy Logic: Theory and ApplicationsThe primary purpose of this book is to provide the reader with a 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. Although it is written as a text for a course at the graduate or upper division undergraduate level, the book is also suitable for self-study and for industry-oriented courses of continuing education. No previous knowledge of fuzzy set theory and fuzzy logic is required for understanding the material covered in the book. Although knowledge of basic ideas of classical (nonfuzzy) set theory and classical (two-valued) logic is useful, fundamentals of these subject areas are briefly overviewed in the book. In addition, basic ideas of neural networks, genetic algorithms, and rough sets are also explained. This makes the book virtually self-contained. Throughout the book, many examples are used to illustrate concepts, methods, and generic applications as they are introduced. Each chapter is followed by a set of exercises, which are intended to enhance readers' understanding of the material presented in the chapter. Extensive and carefully selected bibliography, together with bibliographical notes at the end of each chapter and a bibliographical subject index, is an invaluable resource for further study of fuzzy theory and applications. |

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### Contents

THEORY | 1 |

FUZZY SETS VERSUS CRISP SETS | 35 |

OPERATIONS ON FUZZY SETS | 50 |

Copyright | |

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### Common terms and phrases

applications of fuzzy approximate reasoning Assume basic assignment binary relations bodies of evidence calculate called characterized chromosomes classical concept crisp sets defuzzification degree denote determine engineering equivalence relation evidence theory example expert systems expressed f-conorms f-norm finite focal elements formula fuzzified fuzzy complement fuzzy controllers fuzzy implications fuzzy intersection fuzzy logic fuzzy measure fuzzy measure theory fuzzy numbers fuzzy proposition fuzzy relation equations fuzzy set theory fuzzy systems fuzzy union genetic algorithms Hartley function Hence illustrate inference rules input linguistic terms mathematical matrix membership function membership grade method modus ponens neural networks nonspecificity obtain output parameters partial ordering pattern recognition possibilistic possibility distribution possibility theory probability theory problem properties quantifier real numbers relevant represented respectively Sets and Systems shown in Fig solution standard fuzzy subsets Theorem truth values types uncertainty universal set variable Yager