Interval-Valued Neutrosophic Models Based on Superhypergraphs: Framework and Applications

Abstract

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]. This paper introduces and investigates the interval-valued neutrosophic superhypergraph, a novel structure that unifies interval-valued neutrosophic hypergraphs with neutrosophic superhypergraphs. By assigning intervalvalued neutrosophic triples to each vertex at every hierarchical level, the proposed model accommodates truth, indeterminacy, and falsity degrees within multilevel relationships.