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**A first course in fuzzy logic.
3rd ed.**
*(English)*
Zbl 1083.03031

Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-526-2/hbk). x, 430 p. (2005).

[For reviews of the previous editions see Zbl 0856.03019 and Zbl 0927.03001, respectively.]

This is a mathematically serious introduction to fuzzy sets and their applications at a level of advanced undergraduates or beginning graduates, i.e., it focusses mainly on more elementary aspects of fuzzy sets techniques.

This third edition has been suitably updated and revised. Exercises have been added. There is a new, and rather extended, section on fuzzy sets of type 2. The chapter on possibility theory has been rewritten and extended, as was the chapter on partial knowledge – which treats belief functions and offers the basic facts about rough sets. The chapter on fuzzy integrals has also undergone a larger revision.

The chapter headings are: the concept of fuzziness; some algebra of fuzzy sets; fuzzy quantities; logical aspects of fuzzy sets; basic connectives; additional topics on connectives; fuzzy relations; universal approximation; possibility theory; partial knowledge; fuzzy measures; the Choquet integral; fuzzy modeling and control. There is a suitable bibliography, an index, and answers to selected exercises.

Even if sometimes very concise, this textbook is one of the best suited ones for mathematically oriented people to learn the basic notions and facts about fuzzy sets and their applications.

This is a mathematically serious introduction to fuzzy sets and their applications at a level of advanced undergraduates or beginning graduates, i.e., it focusses mainly on more elementary aspects of fuzzy sets techniques.

This third edition has been suitably updated and revised. Exercises have been added. There is a new, and rather extended, section on fuzzy sets of type 2. The chapter on possibility theory has been rewritten and extended, as was the chapter on partial knowledge – which treats belief functions and offers the basic facts about rough sets. The chapter on fuzzy integrals has also undergone a larger revision.

The chapter headings are: the concept of fuzziness; some algebra of fuzzy sets; fuzzy quantities; logical aspects of fuzzy sets; basic connectives; additional topics on connectives; fuzzy relations; universal approximation; possibility theory; partial knowledge; fuzzy measures; the Choquet integral; fuzzy modeling and control. There is a suitable bibliography, an index, and answers to selected exercises.

Even if sometimes very concise, this textbook is one of the best suited ones for mathematically oriented people to learn the basic notions and facts about fuzzy sets and their applications.

Reviewer: Siegfried J. Gottwald (Leipzig)

### MSC:

03B52 | Fuzzy logic; logic of vagueness |

68T27 | Logic in artificial intelligence |

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

03E72 | Theory of fuzzy sets, etc. |

28E10 | Fuzzy measure theory |

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

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