## 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 xii

The membership function of the fuzzy goal G. The solution of the numerical

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 xx

It rather offers numerical

It rather offers numerical

**examples**wherever possible. I would like to thank very much Mr. C. von Altrock, Ms. B. Lelke, Mr. R. Weber, and Dr. B. Werners for their active participation in preparing this revised edition. Page 4

**Examples**are words such as “birds” (how about penguins, bats, etc.?) or “red roses,” but also terms such as “tall men,” ... An**example**of the latter is the term “creditworthy customers”: A creditworthy customer can possibly be described ... Page 12

**Example**2–1a A realtor wants to classify the house he offers to his clients. One indicator of comfort of these houses is the number of bedrooms in it. Let X = {1, 2, 3, 4, ..., 10} be the set of available types of houses described by x ... Page 13

sha(x)/x.

sha(x)/x.

**Example**2–1d Å = “integers close to 10” A = 0.1/7+0.5/8+0.8/94.1/10+0.8/11+0.5/12+0.1/13**Example**2–1e A = “real numbers close to 10” - 1 A = | —. Tom/. It has already been mentioned that the membership function is not limited ...### 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