Graph theory offers a rigorous framework for modeling relationships and connectivity via vertices and edges 1, 2. Hypergraphs generalize this framework by allowing hyperedges that join more than two vertices 3, 4. Superhypergraphs further enrich the model through iterated powerset constructions, capturing hierarchical and self-referential structures among hyperedges 5. In this paper, we introduce new classes of graphs, namely the Tolerance SuperHyperGraph, Tolerance HyperGraph, Fuzzy Tolerance Hypergraph, and Fuzzy Tolerance SuperHypergraph, and examine their properties.
Tsunenori Fujita (Wed,) studied this question.