Fuzzy Topological Spaces Generated by Fuzzy Digraphs

In this paper, we defined various fuzzy topological spaces on fuzzy digraph and study interrelation between them. Using adjacency relation on fuzzy vertices and fuzzy edges of fuzzy digraph we defined, namely two types of fuzzy topologies, left(right) fuzzy vertex topology and left(right) fuzzy edge topology on fuzzy digraph, respectively. We have obtained results related to fuzzy topology on fuzzy subdigraph [Formula: see text] of fuzzy digraph [Formula: see text]. Separation axioms [Formula: see text], [Formula: see text] and [Formula: see text] for these fuzzy topological spaces are studied. Some characterization results for fuzzy topological spaces related to isomorphic fuzzy digraphs are given. Further, we have shown that two fuzzy digraphs are isomorphic if and only if their corresponding fuzzy topologies are homeomorphic, this relation on set of fuzzy digraphs forms an equivalence relation. We have also defined and studied fuzzy bitopological spaces on fuzzy digraphs.