## 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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Page vii

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**Knowledge**- Based Approaches 302 13.2.3 Neural Net Approaches 304 13.3 Dynamic Fuzzy Data Analysis 306 13.3.1 Problem Description 306 13.3.2 Similarity of Functions 307 13.3.3 Approaches for Analysic Dynamic Systems 313 13.4 Tools for ... Page xi

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**Knowledge**base . 304 304 Basic structure of the**knowledge**- based system . 305 Figure 13-19 ( a ) States of objects at a point of time ; ( b ) projections of trajectories over time into the feature space . 307 Figure 13-20 Structural ... Page xxiv

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**knowledge**discovery . This situation is mirrored in this edition of the book by an extension of the chapter on data mining and a new chapter on fuzzy sets in data bases . The following figure indicates the development of fuzzy set ... Page xxv

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**knowledge**of fuzzy technology and look for new applications in their area . Aachen , April 2001 H.-J. Zimmermann 1 INTRODUCTION TO FUZZY SETS 1.1 Crispness , Vagueness , PREFACE TO THE FOURTH EDITION XXV. Page 6

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**knowledge**about the value of a parameter ( as in tolerance analysis ) . Fuzzy set theory provides a strict mathematical framework ( there is nothing fuzzy about fuzzy set theory ! ) in which vague conceptual phenomena can be precisely ...### 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