## 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 9

**MATHEMATICs**. This first part of this book is devoted to the formal framework of the theory of fuzzy sets. Chapter 2 provides basic definitions of fuzzy sets and algebraic operations that will then serve for further considerations. Page 18

... which is an excellent example for an axiomatic justification of specific

... which is an excellent example for an axiomatic justification of specific

**mathematical**models. We shall therefore sketch their reasoning: Consider two statements, S and T, for which the truth values are pus and pur, respectively, ps, ... Page 20

These requirements, however, are not enough to determine uniquely the

These requirements, however, are not enough to determine uniquely the

**mathematical**form of the complement. Bellman and Giertz require in addition that pus(1/2) = 1/2. Other assumptions are certainly possible and plausible. Exercises 1. Page 22

Departing from the well-established systems of dual logic and Boolean algebra, alternative and additional definitions for terms such as intersection and union, for their interpretation as “and” and “or,” and for their

Departing from the well-established systems of dual logic and Boolean algebra, alternative and additional definitions for terms such as intersection and union, for their interpretation as “and” and “or,” and for their

**mathematical**... Page 24

**mathematical**models can be conceived. These concepts will be discussed in section 3.2. So far we have considered fuzzy sets with crisply defined membership functions or degrees of membership. It is doubtful whether, for instance, ...### What people are saying - Write a review

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### Contents

9 | |

11 | |

16 | |

22 | |

29 | |

Criteria for Selecting Appropriate Aggregation Operators | 43 |

The Extension Principle and Applications | 54 |

Special Extended Operations | 61 |

Applicationoriented Modeling of Uncertainty | 111 |

Linguistic Variables | 140 |

Fuzzy Data Bases and Queries | 265 |

Decision Making in Fuzzy Environments | 329 |

Applications of Fuzzy Sets in Engineering and Management | 371 |

Empirical Research in Fuzzy Set Theory | 443 |

Future Perspectives | 477 |

181 | 485 |

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### Common terms and phrases

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