## 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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**areas**in which the use of the theory of fuzzy sets leads to results that could not be obtained by classical methods ? Professor Zimmermann's treatise provides an affirmative answer to this ques- tion . His comprehensive exposition of ... Page xvii

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**areas**in which fuzzy sets have been applied most extensively is in modeling for managerial decision making . Therefore , this**area**has been selected for more detailed consideration . The information has been divided into two volumes ... Page xviii

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**areas**in more detail and on a more advanced level . The second volume is dedicated to the application of fuzzy set theory to the**area**of human decision making . It is self - contained in the sense that all concepts used are properly ... Page xix

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**areas**. A number of very good books have appeared , primarily dedicated to special**areas**such as Possibility Theory [ Dubois and Prade 1988a ] , Fuzzy Control [ Sugeno 1985a ; Pedrycz 1989 ] , Behavioral and Social Sciences [ Smithson ... Page xx

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**areas**or presenting any mathematical proofs which do not contribute to a better understanding . It rather offers numerical examples wherever possible . I would like to thank very much Mr. C. von Altrock , Ms. B. Lelke , Mr. R. Weber ...### Contents

1 | |

8 | |

22 | |

4 | 44 |

The Extension Principle and Applications | 54 |

Fuzzy Relations on Sets and Fuzzy Sets | 71 |

3 | 82 |

7 | 88 |

Applications of Fuzzy Set Theory | 139 |

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 |

3 | 95 |

4 | 105 |

2 | 122 |

4 | 131 |

Applications of Fuzzy Sets in Engineering and Management | 371 |

Empirical Research in Fuzzy Set Theory | 443 |

Future Perspectives | 477 |

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### Common terms and phrases

a-level aggregation algebraic algorithm applications of fuzzy approach approximately areas base basic Bezdek chapter classical computational concepts considered constraints crisp criteria customers data analysis DataEngine decision defined definition defuzzification degree of membership described determine domain Dubois and Prade elements engineering example expert systems feature formal Fril fuzzy c-means fuzzy clustering fuzzy control fuzzy control systems fuzzy function fuzzy graph fuzzy logic fuzzy measures fuzzy numbers fuzzy relation fuzzy set Ć fuzzy set theory goal inference inference engine input integral intersection interval linear programming linguistic variable Mamdani mathematical measure of fuzziness membership function methods min-operator objective function operators optimal parameters possibility distribution probability probability theory problem properties respect rules scale level scheduling semantic solution structure Sugeno t-conorms t-norms Table tion trajectories truth tables truth values uncertainty vector x₁ Yager Zadeh Zimmermann µĆ(x µµ(x