Path Fuzzy Bitopological Spaces on Fuzzy Directed Graphs

In this paper, we introduce a new concept of fuzzy topological spaces on fuzzy directed graphs by utilizing path relations between vertices and discuss several key results related to fuzzy topological spaces on various fuzzy digraphs. We define strongly connected, symmetric, and asymmetric fuzzy directed graphs, demonstrating that the associated path topological spaces are indiscrete. Furthermore, by employing path fuzzy topological spaces, we define a path fuzzy bitopological space associated with a fuzzy digraph. Various separation axioms, such as fuzzy pairwise \(T₀\), \(T₁\), \(T₂\) and fuzzy pairwise weakly \(T₂\), are studied for path fuzzy bitopological spaces, and the interrelations between path topological spaces and path fuzzy bitopological spaces are examined. This paper also initiates the concept of fuzzy bitopological spaces for fuzzy directed graphs.