Vague Superhypergraph

Abstract

Graph theory examines mathematical structures composed of vertices and edges to model relationships and connectivity.  
Hypergraphs generalize traditional graphs by permitting hyperedges that join more than two vertices simultaneously.  
Superhypergraphs build on this concept by introducing iterated powerset layers, enabling hierarchical and self‐referential connections among hyperedges.  
These ideas have been further refined through frameworks such as fuzzy sets, soft sets, intuitionistic fuzzy sets, neutrosophic sets, vague sets, and plithogenic sets.  

In this paper, we introduce the concept of a vague superhypergraph, which integrates vague-set theory with the superhypergraph formalism.  
We anticipate that this new structure will inspire further research in decision‐making and its diverse applications.