Fuzzy logic with engineering applications.

*(English)*Zbl 0855.93003
New York, NY: McGraw-Hill. xx, 600 p. (1995).

The book can be regarded as an introduction to fuzzy set theory with the main focus on engineering applications of the theory. Chapter 1 introduces the basic notions of fuzzy sets starting from an intuitive background, and contrasts fuzzy sets with other methodologies that help to cope with uncertainty. Fuzzy sets vis-à-vis set theory are studied in Chapter 2. Subsequently, Chapter 3 deals with the notions of fuzzy relations and their calculus. An important issue of membership function estimation is discussed in Chapter 4. Chapter 5 elaborates on the conversions from fuzzy sets to their numerical equivalents (representatives). The extension principle along with the resulting constructions including fuzzy arithmetic are studied in Chapter 6. Two-valued logic and its extensions governed by fuzzy sets are covered in Chapter 7 (more precisely the discussion therein is devoted to many-valued logics – the genuine fuzzy logic has to deal with truth values described via fuzzy truth values). The main applied concepts covered in the book deal with rule-based systems, fuzzy nonlinear models, decision-making, supervised and unsupervised pattern recognition, and fuzzy controllers (Chapters 8-13). There are also a number of miscellaneous topics such as fuzzy optimization, fuzzy regression, and fuzzy measures.

The book elaborates primarily on fuzzy set-based analysis and includes all topics that are usually covered by other textbooks on fuzzy sets. It provides the reader with a wealth of illustrative examples and guides him through a complete process of capturing and quantifying linguistic knowledge as this could be encountered across a number of engineering disciplines. On the other hand, the systematic and comprehensive design procedures are somewhat left out. Moreover, the excessively broad coverage of the book has a negative impact on the depth of the material and this deficiency becomes somewhat visible throughout several sections. As far as the audience is concerned, the book could be a useful reference tool for senior undergraduate courses as well as practicing engineers interested in applying fuzzy set technology.

The book elaborates primarily on fuzzy set-based analysis and includes all topics that are usually covered by other textbooks on fuzzy sets. It provides the reader with a wealth of illustrative examples and guides him through a complete process of capturing and quantifying linguistic knowledge as this could be encountered across a number of engineering disciplines. On the other hand, the systematic and comprehensive design procedures are somewhat left out. Moreover, the excessively broad coverage of the book has a negative impact on the depth of the material and this deficiency becomes somewhat visible throughout several sections. As far as the audience is concerned, the book could be a useful reference tool for senior undergraduate courses as well as practicing engineers interested in applying fuzzy set technology.

Reviewer: W.Pedrycz (Winnipeg)

##### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93A30 | Mathematical modelling of systems (MSC2010) |

93C42 | Fuzzy control/observation systems |

03E72 | Theory of fuzzy sets, etc. |