Chapter 2: Mathematical Representation and Operations in Fuzzy Sets
Chapter 2: Mathematical Representation and Operations 2.1 Introduction Fuzzy sets extend the concept of classical sets by allowing gradual assessment of the membership of elements in a set. Instead of having only two membership values (0 or 1) as in classical set theory, fuzzy sets allow any real number between 0 and 1, enabling a better representation of uncertainty and vagueness. This chapter elaborates on how fuzzy sets are mathematically represented and the various operations that can be performed on them. 2.2 Mathematical Representation of Fuzzy Sets A fuzzy set A in a universe of discourse X is characterized by a membership function: Each element x in X is mapped to a membership value that indicates the degree of membership of x in the fuzzy set A . Example: Let X = {1, 2, 3, 4, 5} Define a fuzzy set A as: This means the element 1 belongs to A with a membership value of 0.1 , and so on. 2.3 Basic Operations on Fuzzy Sets Fuzzy set operations ar...