Fuzzy/Intuitionistic Fuzzy Set Theory

This chapter describes the definition and operations of fuzzy and intuitionistic fuzzy set (IFS) theory with examples. In a fuzzy set, the degree of membership of an element signifies the extent to which the element belongs to a fuzzy set, i.e. there is a gradation of membership value of each element in a set. A membership function is a curve that defines how each point in the input space is mapped to a membership value between 0 and 1. The chapter describes different types of membership functions that may be viewed as mappings of diverse human choices to an interval [0,1]. For constructing an IFS, fuzzy generators are used. Fuzzy generators are a type of fuzzy complements with some conditions. The chapter reviews fuzzy complements. It explains intuitionistic fuzzy operations, relations, compositions, and intuitionistic fuzzy binary relations with examples.