Fuzzy Systems, Modeling and Identification

This text provides an introduction to the use of fuzzy sets and fuzzy logic for the approximation of functions and modeling of static and dynamic systems. The concept of a fuzzy system is first explained. Afterwards, the motivation and practical relevance of fuzzy modeling are highlighted. Two types of rule-based fuzzy models are described: the linguistic (Mamdani) model and the Takagi–Sugeno model. For each model, the structure of the rules, the inference and defuzzification methods are presented. Fuzzy modeling of dynamic systems is addressed, as well as the methods to construct fuzzy models from knowledge and data (measurements). Illustrative examples are given throughout the text. At the end, homework problems are included. MATLAB programs implementing some of the examples are available from the author. The reader is encouraged to study and possibly modify these examples in order to get a better insight in the methods presented. Preface Prerequisites: This text provides an introduction to the use of fuzzy sets and fuzzy logic for the approximation of functions and modeling of static and dynamic systems. It is assumed that the reader has basic knowledge of set and fuzzy set theory (membership functions, operations on fuzzy sets – union, intersection and complement, fuzzy relations, max-min composition, extension principle), mathematical analysis (univariate and multivariate functions, composition of functions), and linear algebra (system of linear equations, least-square solution). Organization. The material is organized in five sections: In the Introduction, different modeling paradigms are first presented. Then, the concept of a fuzzy system is first explained and the motivation and practical relevance of fuzzy modeling are highlighted. Section 2 describes two types of rule-based fuzzy models: the linguistic (Mamdani) model and the Takagi–Sugeno model. For each model, the structure of the rules, the inference and defuzzification methods are presented. At the end of this section, fuzzy modeling of dynamic systems is addressed. In Section 3, methods to construct fuzzy models from knowledge and numerical data are presented. Section 4 reviews some engineering applications of fuzzy modeling, and the concluding Section 5 gives a short summary. Illustrative examples are provided throughout the text, and at the end, homework problems are included. Some of the numerical examples given have been implemented in MATLAB. The code is available from the author on request. The reader is encouraged to study and possibly modify these examples in order to get a better insight in the methods presented. A subject index …