## 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 62

Page vi

... Fuzzy Functions Integration of Fuzzy Functions Integration of a Fuzzy Function over a Crisp

... Fuzzy Functions Integration of Fuzzy Functions Integration of a Fuzzy Function over a Crisp

**Interval**Integration of a (Crisp) Real-Valued Function over a Fuzzy**Interval**Fuzzy Differentiation Uncertainty Modeling Application-oriented ... Page ix

Fuzzy forests. Graphs that are not forests. Maximizing set. A fuzzy function. Triangular fuzzy numbers representing a fuzzy function. The maximum of a fuzzy function. Fuzzily bounded

Fuzzy forests. Graphs that are not forests. Maximizing set. A fuzzy function. Triangular fuzzy numbers representing a fuzzy function. The maximum of a fuzzy function. Fuzzily bounded

**interval**. Uncertainty as situational property. Page xii

Calibration of the

Calibration of the

**interval**for measurement. Subject 34, "Old Man". Subject 58, “Very Old Man". Subject 5, “Very Young Man". Subject 15, “Very Young Man". Subject 17, "Young Man". Subject 32, “Young Man”. Empirical membership functions ... Page 19

The truth value of the “and” and “or” combination of these statements, pu(S and T) and pu(S or T), both from the

The truth value of the “and” and “or” combination of these statements, pu(S and T) and pu(S or T), both from the

**interval**[0, 1], are interpreted as the values of the membership functions of the intersection and union, respectively, ... Page 25

In contrast to the above definition, the membership function of an L-fuzzy set maps into a partially ordered set, L. Since the

In contrast to the above definition, the membership function of an L-fuzzy set maps into a partially ordered set, L. Since the

**interval**[0, 1] is a poset (partially ordered set), the fuzzy set in definition 2–1 is a special L-fuzzy set.### 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