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**Uncertain rule-based fuzzy logic systems: introduction and new directions.**
*(English)*
Zbl 0978.03019

Upper Saddle River, NJ: Prentice Hall. xx, 555 p. (2001).

The monograph presents an approach to fuzzy logic (FL) that can model uncertainties by introducing type-2 FL. Classical FL presented as type-1 FL cannot model uncertainties. It is an application of type-1 FL to rule-based systems. The book deals with such rule-based systems (FLSs) for both type-1 and type-2. It consists of four parts. Part 1 – Preliminaries – consists of 4 Chapters providing background material about uncertainty, membership functions, and two case studies (forecasting of time series and knowledge mining using surveys) that are carried out throughout of the book. Part 2 – Type-1 Fuzzy Logic Systems – contains two Chapters. It provides the underlying basis for the new type-2 FLSs. Type-2 results can be compared with type-1 results on the case studies. Part 3 – Type-2 Fuzzy Sets – contains 3 Chapters, each of which focuses on a different aspect of these sets such as operations and properties, relations and composition, and the concept of a centroid. Part 4 – Type-2 Fuzzy Logic Systems – is the heart of the book consisting of 5 Chapters. 4 Chapters present different architectures for a FLS and how to handle different kinds of uncertainties within them. They concern particularly singleton type-2 FLSs, both type-1 and type-2 non-singledon type-2 FLSs, and the TSK (Takagi-Sugeno-Kang) FLSs. The last Chapter deals with four specific applications of type-2 FLSs. 3 Appendices present: join, meet, and negation operations for non-interval type-2 fuzzy sets; properties of type-1 and type-2 fuzzy sets are given in detail; and finally computation collecting more than 30 MATLAB-type M-files which are available as freeware on the Internet.

The book is an extremely well-readable self-contained text which is carefully balanced between theory and design including worked out numerical examples. Primarily addressed to computer scientists, engineers and mathematicians interested in AI, rule-based systems, and modeling uncertainty, this elegant book supposes only an undergraduate degree of its readers.

The book is an extremely well-readable self-contained text which is carefully balanced between theory and design including worked out numerical examples. Primarily addressed to computer scientists, engineers and mathematicians interested in AI, rule-based systems, and modeling uncertainty, this elegant book supposes only an undergraduate degree of its readers.

Reviewer: LubomĂr Bakule (Barcelona)

### MSC:

03B52 | Fuzzy logic; logic of vagueness |

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

68T27 | Logic in artificial intelligence |

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

03-02 | Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations |

68-02 | Research exposition (monographs, survey articles) pertaining to computer science |