## 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 v

List of Figures List of Tables ForeWord Preface Preface to the Fourth Edition Introduction to Fuzzy Sets Crispness, Vagueness, Fuzziness,

List of Figures List of Tables ForeWord Preface Preface to the Fourth Edition Introduction to Fuzzy Sets Crispness, Vagueness, Fuzziness,

**Uncertainty**Fuzzy Set Theory Fuzzy Mathematics Fuzzy Sets—Basic Definitions Basic Definitions ... Page vi

... Fuzzy Differentiation

... Fuzzy Differentiation

**Uncertainty**Modeling Application-oriented Modeling of**Uncertainty**Causes of**Uncertainty**Type of Available Information**Uncertainty**Methods**Uncertainty**Theories as Transformers of Information Matching**Uncertainty**... Page vii

... Systems Introduction to Expert Systems

... Systems Introduction to Expert Systems

**Uncertainty**Modeling in Expert Systems Applications Fuzzy Control Origin and Objective Automatic Control The Fuzzy Controller Types of Fuzzy Controllers The Mamdani Controller Defuzzification ... Page xiii

Rough taxonomy of

Rough taxonomy of

**uncertainty**properties. Possibility functions. Koopman's vs. Kolmogoroff's probabilities. Relationship between Boolean algebra, probabilities, and possibilities. Formal quality of implication operators. Expert systems. Page xvi

The concept of possibility plays a particularly important role in the representation of meaning, in the management of

The concept of possibility plays a particularly important role in the representation of meaning, in the management of

**uncertainty**in expert systems, and in applications of the theory of fuzzy sets to decision analysis.### 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