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**Fuzzy set theory – and its applications.
4th ed.**
*(English)*
Zbl 0984.03042

Dordrecht: Kluwer Academic Publishers. xxv, 514 p. (2002).

[For reviews of earlier editions see Zbl 0719.04002 and Zbl 0845.04006.]

This is the fourth edition of the classic and highly acclaimed book on fuzzy sets and their applications. In comparison to the previous editions, the material has been augmented at the applied side of the studies on fuzzy sets. The material is structured into two parts. The first part serves as a thorough yet quite condensed and focused introduction to the fundamentals of fuzzy sets and covers the key topics of basic definitions, generalizations of fuzzy sets, fuzzy measures and measures of fuzziness, fuzzy graphs and relations, possibility measure and fuzzy analysis (e.g., extension principle, fuzzy functions and fuzzy numbers). The second part is a carefully organized overview of the main areas of applications. This material is of particular value to those interested in the applied side of fuzzy sets. Undoubtedly, the book points at the evident diversity of the application areas while at the same time emphasizing the omnipresent visibility of fuzzy sets as the conceptually rich information technology that cuts across these different disciplines. The list is long: approximate reasoning, expert systems, fuzzy control, fuzzy databases, decision making, scheduling, mathematical programming, logistics, fault detection, to name the most representative items. In comparison to the previous editions, the book identifies new trends such as fuzzy data analysis (that becomes more profound in light of the recent developments occurring in data mining), emphasizes the empirical facet of research in fuzzy sets and includes an interesting and thought provoking section on future perspectives of the technology of fuzzy sets.

Overall, this lucidly written, comprehensive, and carefully balanced book is a must for everybody pursuing research in fuzzy sets and interested in their applications.

This is the fourth edition of the classic and highly acclaimed book on fuzzy sets and their applications. In comparison to the previous editions, the material has been augmented at the applied side of the studies on fuzzy sets. The material is structured into two parts. The first part serves as a thorough yet quite condensed and focused introduction to the fundamentals of fuzzy sets and covers the key topics of basic definitions, generalizations of fuzzy sets, fuzzy measures and measures of fuzziness, fuzzy graphs and relations, possibility measure and fuzzy analysis (e.g., extension principle, fuzzy functions and fuzzy numbers). The second part is a carefully organized overview of the main areas of applications. This material is of particular value to those interested in the applied side of fuzzy sets. Undoubtedly, the book points at the evident diversity of the application areas while at the same time emphasizing the omnipresent visibility of fuzzy sets as the conceptually rich information technology that cuts across these different disciplines. The list is long: approximate reasoning, expert systems, fuzzy control, fuzzy databases, decision making, scheduling, mathematical programming, logistics, fault detection, to name the most representative items. In comparison to the previous editions, the book identifies new trends such as fuzzy data analysis (that becomes more profound in light of the recent developments occurring in data mining), emphasizes the empirical facet of research in fuzzy sets and includes an interesting and thought provoking section on future perspectives of the technology of fuzzy sets.

Overall, this lucidly written, comprehensive, and carefully balanced book is a must for everybody pursuing research in fuzzy sets and interested in their applications.

Reviewer: Witold Pedrycz (Edmonton)

### MSC:

03E72 | Theory of fuzzy sets, etc. |

03-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations |

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |

68Txx | Artificial intelligence |

28E10 | Fuzzy measure theory |

68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |

93C42 | Fuzzy control/observation systems |

68T10 | Pattern recognition, speech recognition |

03B52 | Fuzzy logic; logic of vagueness |

91B06 | Decision theory |

90B99 | Operations research and management science |