A Model of Intuitionistic Fuzzy Soft Super-Hypergraphs with Illustrative Applications (European Journal of Pure and Applied Mathematics, 2026)
Graph theory provides a fundamental framework for modeling relationships using vertices and edges. Hypergraphs extend this framework by permitting hyperedges that connect any number of vertices simultaneously, and Super-hypergraphs further generalize hypergraphs through iterated powerset constructions to represent hierarchical connections. Concurrently, a variety ofuncertainty-modeling paradigms—such as fuzzy sets, soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy offsets, hyper-intuitionistic fuzzy sets, and intuitionistic fuzzy multidirected sets—have enriched classical graph concepts. In this paper, we introduce the Intuitionistic Fuzzy Soft n-Super-hypergraph, a unified n-th order structure that seamlessly integrates intuitionistic fuzzy Super-hypergraphs with soft Superhypergraphs. We present rigorous definitions, explore key structural properties, and highlight potential applications in decision-making under uncertainty, demonstrating how this framework effectively captures both complex hierarchical organization and nuanced uncertainty in real-world networks.
Keywords: Fuzzy Set; Soft Graph; SuperHyperGraph