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

Mendel, Jerry M.

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.

Reviewer: Lubomír 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

Keywords:

rule-based fuzzy logic systems; uncertainty; type-1 and type-2 membership functions; type-1 fuzzy logic; type-2 fuzzy logic; forecasting of time series; knowledge mining using surveys

Software:

Matlab