## 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

Results 1-5 of 82

Page vi

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**Rules**170 9.5.3 Inference Methods in Fril 172 9.5.4 Fril Inference for a Single**Rule**175 9.5.5 Multiple**Rule**Case 176 9.5.6 Interval and Point Semantic Unification 177 9.5.7 9.5.8 Least Prejudiced Distribution and Learning Applications ... Page vii

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**Rules**242 11.6 Adaptive Fuzzy Control 243 11.7 Applications 244 11.7.1 Crane Control 244 11.7.2 Control of a Model Car 246 11.7.3 Control of a Diesel Engine 248 11.7.4 Fuzzy Control of a Cement Kiln 249 11.8 Tools 255 11.9 Stability 257 ... Page x

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**Rule**consequences in the heating system example . Extreme Value Strategies . 232 234 Figure 11-6 COA Defuzzification . 235 Figure 11-7 Neighboring membership functions . 236 Figure 11-8 Separate membership functions . 236 Figure 11-9 ... Page xii

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**rules**. Example of an FMS [ Hartley 1984 , p . 194 ] . 404 405 Figure 15-20 Criteria hierarchies . ( a ) Release scheduling ; ( b ) Machine scheduling . 407 Figure 15-21 Principle of approximate reasoning . 409 Figure 15-22 Figure 15-23 ... Page xiv

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**rules**. Membership grades for the**rules**. Definition of linguistic variables [ Rinks 1982 ] . Membership functions . Cost results . Comparison of performances . Structure of instruction program . Availability of instructors ...### 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