## 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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**containing**trajectories into trajectories into a usual feature vector . 311 314 Figure 13-25 Input and output of the functional fuzzy c - means . 315 Figure 13-26 Structure of DataEngine . 318 Figure 13-27 Screen shot of DataEngine ... Page xvii

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**containing**specialized contri- butions or monographs that focus only on specific areas of fuzzy sets , such as pattern recognition [ Bezdek 1981 ] , switching functions [ Kandel and Lee ...**contains**the basic theory of Preface Preface. Page xviii

Hans-Jürgen Zimmermann. volumes . The first volume

Hans-Jürgen Zimmermann. volumes . The first volume

**contains**the basic theory of fuzzy sets and some areas of application . It is intended to provide extensive coverage of the theoretical and applicational approaches to fuzzy sets ... Page 1

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**contains**no ambiguities . Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known , and that there are no doubts about their values or their occurrence . If the model under ... Page 8

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**containing**chapters 2 to 8 , will develop the formal frame- work of fuzzy mathematics . Due to space limitations and for didactical reasons , two restrictions will be observed : 1. Topics that are of high mathematical interest but ...### 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