Introduction

This chapter describes what this book is about. Its coverage includes: rules; four kinds of uncertainty partitions—crisp, first-order, second-order with uniform weighting, and second-order with non-uniform weighting—and that they can be, respectively, mathematically modeled using classical (crisp) set theory, classical (type-1) fuzzy set theory, interval type-2 fuzzy set theory, and general type-2 fuzzy set theory; structure of a rule-based fuzzy system and explanation of its four components—rules, fuzzifier, inference and output processor; why type-2 fuzzy sets are a new direction for fuzzy systems; the fundamental design requirement of a type-2 fuzzy system; advisable design approaches; understanding the potential for improved performance of the different kinds of fuzzy systems; explainable fuzzy systems; an impressionistic brief history of type-1 fuzzy sets and fuzzy logic; the early literature (1975–1992) about type-2 fuzzy sets and systems, and the literature that was heavily used when the first edition of this book was written; coverage of Chaps. 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , and 11 ; applicability of the book’s contents outside of the field of rule-based fuzzy systems; and a list of sources that are available for software that can be used to implement much of what is in this book.