## Fuzzy Set Theory—and Its ApplicationsSince its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, robotics, and others. Theoretical advances have been made in many directions. The primary goal of Fuzzy Set Theory - and its Applications, Fourth Edition is to provide a textbook for courses in fuzzy set theory, and a book that can be used as an introduction. To balance the character of a textbook with the dynamic nature of this research, many useful references have been added to develop a deeper understanding for the interested reader. Fuzzy Set Theory - and its Applications, Fourth Edition updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. Chapters have been updated and extended exercises are included. |

### From inside the book

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### Contents

Introduction to Fuzzy Sets | 1 |

Extensions | 23 |

4 | 44 |

The Extension Principle and Applications | 55 |

Fuzzy Relations on Sets and Fuzzy Sets | 71 |

Fuzzy Analysis | 93 |

4 | 105 |

Uncertainty Modeling | 111 |

3 | 154 |

4 | 160 |

5 | 169 |

Fuzzy Sets and Expert Systems | 185 |

Fuzzy Control | 223 |

Fuzzy Data Bases and Queries | 265 |

Decision Making in Fuzzy Environments | 329 |

Applications of Fuzzy Sets in Engineering and Management | 371 |

2 | 122 |

4 | 131 |

Applications of Fuzzy Set Theory | 139 |

Empirical Research in Fuzzy Set Theory | 443 |

Future Perspectives | 477 |

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### Common terms and phrases

aggregation algorithm analysis applications approach appropriate approximately areas assignment assume base basic called chapter classical clustering computational concepts considered constraints contains crisp criteria customers decision defined definition degree of membership depends described determine discussed distribution elements engineering example exist expert systems expressed extension Figure formal fuzzy control fuzzy numbers fuzzy set theory given goal human important indicate inference instance integral interpreted intersection interval knowledge language linguistic variable logic mathematical mean measure membership function methods objective observed obtain operators optimal positive possible Prade probability problem programming properties provides reasoning relation relationship representing require respect rules scale shown shows similarity situation solution space specific statement structure suggested t-norms Table tion true truth uncertainty union values Zadeh Zimmermann