Fuzzy set is a set containing the elements that have varying degree of membership. Fuzzy sets support a flexible sense of membership values of elements of a set.

The membership function μA(x) is associated with a fuzzy set A, such that the membership function maps every element of universal set ‘X’ to the interval [0,1] ↔ 0 ≤ μA(x) ≤ 1

It can also be written as μA(x) : X → [0, 1]

A fuzzy set can also be defined as follow:

“If X is universe of discourse, x is a particular element of ‘X’, then a fuzzy set A~ (tilde understroke) defined on X may be written as collection of ordered pairs:

The membership function μA(x) may be described by discrete values or by a continuous function.