• Jerry M. Mendel


This chapter describes what this book is about. It explains four kinds of uncertainty partitions—crisp, first-order, second-order with uniform weighting, and second-order with nonuniform 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; provides the structure of a rule-based fuzzy system, and explains its four components—rules, fuzzifier, inference, and output processor; explains why type-2 fuzzy sets are a new direction for fuzzy systems; states and explains the fundamental design requirement of a type-2 fuzzy system; provides an impressionistic brief history of type-1 fuzzy sets and fuzzy logic; reviews the early literature (1975–1992) about type-2 fuzzy sets and systems (the literature that was heavily used when the first edition of this book was written), and some literature about applications of type-2 fuzzy set and systems; and provides a brief summary of what is covered in Chaps.  2 11, a very short statement about the applicability of the book’s coverage 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.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

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