## Fuzzy Set Theory and Its Applications |

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### Contents

Introduction to Fuzzy Sets | 1 |

Extensions | 23 |

Fuzzy Measures and Measures of Fuzziness | 45 |

Fuzzy Relations and Fuzzy Graphs | 69 |

Fuzzy Analysis | 91 |

Possibility Theory Probability Theory and Fuzzy Set | 109 |

Applications of Fuzzy Set Theory | 129 |

Expert Systems and Fuzzy Control | 171 |

### Common terms and phrases

a-level aggregation algebraic algorithm alternative applications of fuzzy approach areas assignment assume base Bezdek chapter clustering compute concepts considered constraints crisp criteria criterion decision maker defined definition degree of membership denotes described determined Dubois and Prade empirical evaluation 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 inference integral interpreted intersection interval knowledge linear programming linguistic variable logic programming mathematical matrix max-min maximize maximum 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 solution space statements structure subset symmetric true truth tables truth values uncertainty Yager young Zadeh Zimmermann