Hierarchical Network Modeling with Intuitionistic Fuzzy Superhypergraphs

Abstract

Traditional graphs capture only pairwise relationships, whereas hypergraphs allow edges to connect arbitrary subsets of vertices, modeling higher-order interactions. Superhypergraphs extend this idea further by iteratively applying the powerset operation to reveal nested, hierarchical connections. Concurrently, fuzzy‐logic theories such as fuzzy sets and intuitionistic fuzzy sets—provide graded notions of membership and uncertainty. Despite the individual success of these frameworks, the combination of hierarchical superhypergraph structures with intuitionistic fuzziness has received little attention. In this paper, we introduce the intuitionistic fuzzy superhypergraph, in which each supervertex and superedge carries both membership and non-membership degrees subject to Atanassov’s constraint. We establish its formal properties, present an efficient construction algorithm, and demonstrate how it can underpin a novel decision-making procedure for complex, uncertain, multi-scale networks.