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.