Directed n-Superhypergraphs Incorporating Bipolar Fuzzy Information: A Multi-Tier Framework for Modeling Bipolar Uncertainty in Complex Networks

Abstract

 Graph theory studies the mathematical structures of vertices and edges to model relationships and
 connectivity. Hypergraphs extend this framework by allowing hyperedges to connect arbitrarily many vertices at
 once [1], and Super-HyperGraphs further generalize hypergraphs via iterated powerset constructions to capture
 hierarchical linkages among edges [2,3]. Bipolar fuzzy directed graphs assign positive and negative member
ship degrees to directed edges and vertices, and bipolar fuzzy directed hypergraphs extend this assignment to
 multi-vertex hyperedges. In this paper, we extend directed Super-HyperGraphs by incorporating bipolar fuzzy
 membership and introduce the Bipolar Fuzzy Directed n-Super-HyperGraph, whose structural properties we
 investigate.

DOI: 10.5281/zenodo.15775233