Graph theory provides a mathematical framework for representing relationships and connectivity through vertices and edges 1,2. Hypergraphs extend this classical notion by introducing hyperedges that may connect more than two vertices at once 3. Superhypergraphs further enrich the model by employing iterated powerset constructions, thereby capturing hierarchical and self-referential structures among hyperedges 4, 5. A fuzzy 𝑛-SuperHyperGraph advances this approach by assigning membership degrees to both supervertices and superedges, offering a flexible tool for modeling uncertainty in complex systems. In this paper, we propose an extension of this framework, termed the Fuzzy Off-SuperHyperGraph, which integrates the offgraph paradigm into fuzzy 𝑛-SuperHyperGraphs. We establish its formal definition, investigate its structural properties, and discuss its potential applications in uncertainty modeling and hierarchical network analysis.
Tsunenori Fujita (Tue,) studied this question.