Fuzzy set Properties/ Operations

Fuzzy Set Operations

Fuzzy union (U): the union of two fuzzy sets is the maximum (MAX) of each element from two sets.

E.g.

A = {1.0, 0.20, 0.75}

B = {0.2, 0.45, 0.50}

A È B = {MAX(1.0, 0.2), MAX(0.20, 0.45), MAX(0.75, 0.50)} = {1.0, 0.45, 0.75}

Fuzzy intersection (Ç): the intersection of two fuzzy sets is just the MIN of each element from the two sets.

E.g.A B = {MIN(1.0, 0.2), MIN(0.20, 0.45), MIN(0.75, 0.50)} = {0.2, 0.20, 0.50}

Complement ( _c): The complement of a fuzzy set is composed of all elements’ complement.

The complement of a fuzzy variable with DOM x is (1-x).

Example.

Ac = {1 – 1.0, 1 – 0.2, 1 – 0.75} = {0.0, 0.8, 0.25}