Embedding b-Metric Spaces of Reducible Fuzzy Digraphs into Normed Spaces

In traditional and iterative algebraic techniques, representing fuzzy digraphs using their adjacency matrices can pose challenges, particularly when dealing with graphs featuring an extensive quantity of nodes or edges. These difficulties are especially pronounced in graphs that do not necessarily exhibit strong connectivity between nodes, which are known as reducible digraphs. In this study, we explore different structure of reducible fuzzy digraphs, employing an innovative b-metric structure. This structure enhances the embedding of massive data entities or nodes into low-dimensional realm depicted by a normed space. Therefore, our aim is to define a novel notion of a distance function called bRD-distance between any two vertices (or nodes) in reducible fuzzy digraphs and utilize it to introduce quasi-pseudo- b-metric spaces for these digraphs. Furthermore, to minimize bRD-distance calculations, we demonstrate the process of embedding such bRD-metrics on reducible fuzzy graphs into the designated normed space ℓ∞. Ultimately, a computational example, real-world application, and comparative evaluation confirm the practicality of the suggested technique in handling reducibility, asymmetry, and vagueness in fuzzy digraphs.