ABSTRACT
Fuzzy set theory was first proposed by L. A. Zadeh in 1965 as a way to characterize nonprobabilistic uncertainties. In this section, we introduce the principal concepts and mathematical notations of fuzzy set theory and fuzzy inference system. Various fuzzy set operations are explained with graphical illustrations. The basic concepts and operations on fuzzy relations are presented. The set–relation and relation– relation compositions and their usage in the compositional rule of inference are explained, which play an important role in various research areas such as fuzzy system analysis, design of fuzzy controllers, and decision-making processes. The basic architecture and the design methodology of a fuzzy inference system are presented with practical examples. The content is explained in clear notations to facilitate readers’ easy reading and can be served as an introductory foundation to understanding various techniques on fuzzy modeling and control later in this book.
