## 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 vii

... Methods for Fuzzy Data Analysis Algorithmic Approaches Knowledge-Based Approaches Neural Net Approaches Dynamic Fuzzy Data Analysis

... Methods for Fuzzy Data Analysis Algorithmic Approaches Knowledge-Based Approaches Neural Net Approaches Dynamic Fuzzy Data Analysis

**Problem**Description Similarity of Functions Approaches for Analysic Dynamic Systems Tools for Fuzzy ... Page viii

... in Logistics Fuzzy Approach to the Transportation

... in Logistics Fuzzy Approach to the Transportation

**Problem**Fuzzy Linear Programming in Logistics Fuzzy Sets in Scheduling Job-Shop Scheduling with Expert Systems A Method to Control Flexible Manufacturing Systems Aggregate Production ... Page xi

The vector-maximum

The vector-maximum

**problem**. Fuzzy LP with min-operator. Fuzzy sets representing weights and ratings. Final ratings of alternatives. Preferability of alternative 2 over all others. Linguistic values for variable “rigidity". Page xiv

Table of the parametric transportation

Table of the parametric transportation

**problem**. Solution to transportation**problem**. Membership grades for slack time and waiting time. Membership grades for conditional parts of the rules. Membership grades for the rules. Results. Page xv

Nevertheless, a question that is frequently raised by the skeptics is: Are there, in fact, any significant

Nevertheless, a question that is frequently raised by the skeptics is: Are there, in fact, any significant

**problem**-areas in which the use of the theory of fuzzy sets leads to results that could not be obtained by classical methods?### What people are saying - Write a review

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### Contents

9 | |

Fuzzy Control | 11 |

Basic SetTheoretic Operations for Fuzzy Sets | 16 |

Extensions | 22 |

SetTheoretic Operations | 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