A Framework of M -Polar Fuzzy and q-Rung Orthopair Fuzzy n-SuperHyperGraphs with Some Applications

Authors

  • Takaaki Fujita * Independent Researcher

https://doi.org/10.48314/tsc.vi.31

Abstract

Graph theory studies mathematical structures of vertices and edges to model relationships and connectivity
[1]. Hypergraphs extend traditional graphs by allowing hyperedges that connect any number of vertices
simultaneously [2]. Superhypergraphs further generalize this idea through iterated powerset layers, enabling
hierarchical and self-referential connections among hyperedges [3, 4]. These concepts have been enriched
by uncertainty frameworks such as fuzzy sets [5], soft sets [6], intuitionistic fuzzy sets [7], neutrosophic
sets [8], vague sets [9], hesitant fuzzy sets [10], and plithogenic sets [11].
In this paper, we introduce the notion of an M-polar fuzzy n-SuperHypergraph and, in particular, the
q-Rung Orthopair fuzzy n-SuperHypergraph, which unifies vague-set theory with the superhypergraph
formalism. We anticipate that this new structure will inspire further research in decision-making and its
diverse applications. 

Keywords:

Graph Theory, SuperHyperGraph, Fuzzy Set, q-Rung Orthopair Fuzzy Graph

Published

2025-08-30

Issue

Section

Articles

How to Cite

Fujita, T. (2025). A Framework of M -Polar Fuzzy and q-Rung Orthopair Fuzzy n-SuperHyperGraphs with Some Applications. Transactions on Soft Computing . https://doi.org/10.48314/tsc.vi.31