## 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. |

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Page xi

Transformation of a feature vector

Transformation of a feature vector

**containing**trajectories into trajectories into a usual feature vector. Input and output of the functional fuzzy c-means. Structure of DataFngine. Screen shot of DataBngine. Cracking furnace. Page xvii

Existing books are edited volumes

Existing books are edited volumes

**containing**specialized contributions or monographs that focus only on specific areas of fuzzy sets, such as pattern recognition [Bezdek 1981), switching functions [Kandel and Lee 1979), ... Page xviii

The first volume

The first volume

**contains**the basic theory of fuzzy sets and some areas of application. It is intended to provide extensive coverage of the theoretical and applicational approaches to fuzzy sets. Sophisticated formalisms have not been ... Page 1

Generally, precision also implies that the model is unequivocal, that is, that it

Generally, precision also implies that the model is unequivocal, that is, that it

**contains**no ambiguities. Certainty eventually indicates that we assume the structures and parameters of the model to be definitely known, and that there ... Page 8

The present book will therefore proceed as follows: Part I of this book,

The present book will therefore proceed as follows: Part I of this book,

**containing**chapters 2 to 8, will develop the formal framework of fuzzy mathematics. Due to space limitations and for didactical reasons, two restrictions will be ...### 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