Fuzzy set operations are extensions of classical set operations, incorporating degrees of membership. These operations include union, intersection, complement, and more.

1. Union (OR):

Definition: The union of two fuzzy sets and is a fuzzy set , where the membership degree of each element in is the maximum of its membership degrees in and .

Formula:

Example: If and , then .

1. Intersection (AND):

Definition: The intersection of two fuzzy sets and is a fuzzy set , where the membership degree of each element in is the minimum of its membership degrees in and .

Formula:

Example: If and , then .

1. Complement (NOT):

Definition: The complement of a fuzzy set is a fuzzy set , where the membership degree of each element in is minus its membership degree in .

Formula:

Example: If , then .

1. Difference (A - B):

Definition: The difference of fuzzy sets and is a fuzzy set , where the membership degree of each element in is the membership of the element in reduced by its membership in .

Formula: