## 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

Page xxi

Since 1994, fuzzy set theory, artificial neural nets, and genetic algorithms have also moved closer together and are now normally

Since 1994, fuzzy set theory, artificial neural nets, and genetic algorithms have also moved closer together and are now normally

**called**“computational intelligence.” All these changes have made this technology more powerful but also ... Page 4

...

...

**called**a “subjective category,” becomes fuzzy. One could imagine that the subjective category “creditworthiness” is decomposed into two smaller subjective categories, each of which needs fewer descriptors to be completely described. Page 11

... of membership for the elements of a given set. Definition 2–1 If X is a collection of objects denoted generically by x, then a fuzzy set A in X is a set of ordered pairs: A ={(x, us(x)|xe X} pi(x) is

... of membership for the elements of a given set. Definition 2–1 If X is a collection of objects denoted generically by x, then a fuzzy set A in X is a set of ordered pairs: A ={(x, us(x)|xe X} pi(x) is

**called**the membership function. Page 12

A ={(x, us(x)|xe X} pi(x) is

A ={(x, us(x)|xe X} pi(x) is

**called**the membership function or grade of membership (also degree of compatibility or degree of truth) of x in A that maps X to the membership space M (When M contains only the two points 0 and 1, ... Page 13

If suppla(x) = 1, the fuzzy set A is

If suppla(x) = 1, the fuzzy set A is

**called**normal. A nonempty fuzzy set A can always be normalized by dividing pi(x) by suppli(x). As a matter of convenience, we will generally assume that fuzzy sets are normalized.### What people are saying - Write a review

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### Contents

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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