The fuzzy set concept was introduced by Zadeh [12] in 1965. In 1975, Rosenfeld [8] introduced the concept of a fuzzy graph. Many of the crisp graph concepts have been extended to fuzzy graph theory. In this paper, we are studying the isomorphism and its types for the fuzzy graph such that weak, co-weak. On the other hand, we are investigating the fuzzy graph complement and the relation between the fuzzy graph and its complement by the isomorphic.

fuzzy sets, fuzzy graph, weak isomorphism, co-weak isomorphism, complementary fuzzy graph, self complementary fuzzy graph, isomorphic fuzzy graph.