What is a Fuzzy Relation and Mention the Operations on Fuzzy Relations

Fuzzy Relations :-

A fuzzy relation R is a mapping from Cartesian space X x Y to the interval [0, 1] where the strength of mapping is expressed by membership function of the relation µR(x, y).

Operations on Fuzzy Relations :-

Let R and S be two fuzzy relations on Cartesian space X x Y. Then the membership functions of the operations union, intersection, compliment and containment on these two fuzzy relations are as follows:

Union

Union of Fuzzy Relations

Intersection

Intersection of Fuzzy Relations

Compliment

Compliment of a Fuzzy Relation R

Containment

Containment on Fuzzy Relations R and S