Basic Fuzzy Mathematics for Fuzzy Control and Modeling

Fuzzy control and modeling use only a small portion of the fuzzy mathematics that is available; this portion is also mathematically quite simple and conceptually easy to understand. In this chapter, we introduce some essential concepts, terminology, notations, and arithmetic of fuzzy sets and fuzzy logic. We include only a minimum though adequate amount of fuzzy mathematics necessary for understanding fuzzy control and modeling. To facilitate easy reading, these background materials are presented in plain English and in a rather informal manner with simple and clear notation as well as explanation. Whenever possible, excessively rigorous mathematics is avoided. The materials covered in this chapter are intended to serve as an introductory foundation for the reader to understand not only the fuzzy controllers and models in this book but also many others in the literature.