Fuzzy Logic

Non-interactive fuzzy sets can be thought of analogous to independent events in probability theory. Which means the occurrence of one event is not dependent on the occurrence of others. Fuzzy set ‘A’ is separable into two non-interactive fuzzy sets called

Any relation between two sets X, Y is known as binary relation. When X ≠ Y, binary relation R(X,Y) is called bipartitie graph. Whereas if X = Y, then R(X,Y) is called directed or di-graph. Binary relations are represented by

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

A binary fuzzy relation R is represented by x R y where (x, y) ∈ R(X, Y). In-detail it will be represented by α / xRy where µR(x, y) = α The domain of a fuzzy relation R(X, Y) is