Revealing Hierarchical Uncertainty with Quadri- and PentaPartitioned Neutrosophic HyperGraphs and SuperHyperGraphs

Graph theory offers a foundational framework for modeling relationships through vertices and edges [1, 2]. Hypergraphs broaden this framework by introducing hyperedges that link multiple vertices simultaneously [3], whereas superhypergraphs further generalize hypergraphs via iterated powerset constructions, thereby capturing intricate hierarchical dependencies [4, 5]. In this paper, we introduce Quadri-and PentaPartitioned Neutrosophic HyperGraphs and SuperHyperGraphs. These novel structures extend standard hypergraphs and superhypergraphs by integrating Quadripartitioned and Pentapartitioned Neutrosophic Sets, respectively, to capture multi-dimensional uncertainty at both vertex and hyperedge levels. The resulting frameworks hold promise for more efficient decision-making in complex networked systems.