## 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 vi

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

... 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 vii

... Tools Stability Extensions Fuzzy Data Bases and Queries Introduction Fuzzy Relational Databases Fuzzy Queries in

... Tools Stability Extensions Fuzzy Data Bases and Queries Introduction Fuzzy Relational Databases Fuzzy Queries in

**Crisp**Databases Fuzzy Data Analysis Introduction Methods for Fuzzy Data Analysis Algorithmic Approaches Knowledge-Based ... Page viii

... with

... with

**Crisp**Objective Function Fuzzy Dynamic Programming Fuzzy Dynamic Programming with**Crisp**State Transformation Function Fuzzy Multicriteria Analysis Multi Objective Decision Making (MODM) Multi Attributive Decision Making (MADM) ... Page xi

**Crisp**clusters of the butterfly. Cluster 1 of the butterfly. Cluster 2 of the butterfly. Clusters for m = 1.25. Clusters for m = 2. Clusters by the FSC. (a) Data set; (b) circles found by FSC; ... Page xv

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**crisp**sets relates to the combination of fuzzy sets through disjunction and conjunction or, equivalently, union and intersection. Professor Zimmermann and his associates at the Technical University of Aachen have made many important ...### What people are saying - Write a review

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### Contents

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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