Neutrosophic Soft n-Super-HyperGraphs with Real-World Applications

Graph theory provides a fundamental framework for modeling relationships using vertices and edges [1, 2]. Hypergraphs extend this framework by allowing hyperedges that can simultaneously connect multiple vertices [3], while n-Super-HyperGraphs further generalize hypergraphs via iterated power-set constructions to capture hierarchical relationships [4, 5]. In parallel, variousuncertainty modeling paradigms—such as fuzzy sets [6], soft sets [7], intuitionistic fuzzy sets [8–10], neutrosophic sets, and plithogenic sets—have been developed to handle imprecise or indeterminate information. In this paper, we propose a novel framework called the Neutrosophic Soft n-Super-HyperGraph, which integrates neutrosophic logic, soft set theory, and n-Super-HyperGraph structures. This model has the potential to facilitate effective decision-making in complex and uncertain networkedenvironments.