Chapter 2 - Fuzzy Logic: A Specialized Tutorial

Abstract

This chapter discusses the term “fuzzy logic,” as currently used in the literature. It has two distinct meanings: In the narrow sense, it is viewed as a generalization of the various many-valued logics that have been investigated in the area of mathematical logic since the beginning of the 20th century, whereas in the alternative, broad sense, fuzzy logic is viewed as a system of concepts, principles, and methods for dealing with modes of reasoning that are approximate rather than exact. The logic of this broad sense is discussed in the chapter. Fuzzy set theory is an outgrowth of classical set theory. Contrary to the classical concept of a set, or crisp set, the boundary of a fuzzy set is not precise. In this sense, fuzzy logic is based upon fuzzy set theory. It utilizes the apparatus of fuzzy set theory for formulating various forms of sound approximate reasoning in natural language. Operations on fuzzy sets possess a considerably greater variety than those on classical sets. There are five types of operations on fuzzy sets that are currently recognized: modifiers, compliments, intersections, unions, and averaging operations.