## 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 85

Page xv

In recent years, this issue has

In recent years, this issue has

**given**rise to an extensive literature dealing with t-norms and related concepts that link some aspects of the theory of fuzzy sets to the theory of probabilistic metric spaces developed by Karl Menger. Page 11

For a fuzzy set, the characteristic function allows various degrees of membership for the elements of a

For a fuzzy set, the characteristic function allows various degrees of membership for the elements of a

**given**set. Definition 2–1 If X is a collection of objects denoted generically by x, then a fuzzy set A in X is a set of ordered ... Page 25

A more general definition of a fuzzy set than is

A more general definition of a fuzzy set than is

**given**in definition 2–1 is that of an L-fuzzy set [Goguen 1967; De Luca and Termini 1972). In contrast to the above definition, the membership function of an L-fuzzy set maps into a ... Page 27

Pawlak [1985] shows that the concept of approximation

Pawlak [1985] shows that the concept of approximation

**given**by the equivalence relation R and the approximation space may not, in general, be replaced by a membership function similar to that introduced by Zadeh.Page 35

You have reached your viewing limit for this book.

You have reached your viewing limit for this book.

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

### Other editions - View all

### 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