## 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 xii

The membership function of the fuzzy

The membership function of the fuzzy

**goal**G. The solution of the numerical example. Structure of OPAL. Fuzzy sets for the ratio in the “if” part of the rules. Example of an FMS [Hartley 1984, p. 194]. Criteria hierarchies. Page xiii

Ratings and weights of alternative

Ratings and weights of alternative

**goals**. Selected applications in management and engineering. Experimental Data. Surface quality parameters (output data). Boundary values of the linguistic variable “significance". Page xvii

The primary

The primary

**goal**of this book is to help to close this gap—to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. One of the areas in which fuzzy sets have been applied most extensively is ... Page 4

The achievement potential is based on mental and physical capacity as well as on the individual's motivation. The business conduct includes economical standards. While the former means the setting of realistic

The achievement potential is based on mental and physical capacity as well as on the individual's motivation. The business conduct includes economical standards. While the former means the setting of realistic

**goals**, reasonable planning ... Page 6

In this context it may be useful to cite and comment the major

In this context it may be useful to cite and comment the major

**goals**of this technology briefly and to correct the still ... I am not sure, however, whether it can (still) be considered to be the most important**goal**of fuzzy set theory.### 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