New classes of graphs, including fuzzy tolerance hypergraphs and superhypergraphs, enrich graph theory by capturing complex relationships.
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.
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Tsunenori Fujita (2025) studied this question.
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