Recursive Neutrosophic SuperHypergraphs with Illustrative Applications

Authors

• Takaaki Fujita, Independent Researcher, Tokyo, JapanFollow
• Ajoy Kanti Das, Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, IndiaFollow
• Suman Das, Assistant Professor Grade II (Mathematics), Department of Education, National Institute of Technology Calicut, Kozhikode-673601, Kerala, IndiaFollow
• Sankar Prasad Mondal, Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata-741249, West Bengal, IndiaFollow
• Volkan Duran, Department of Computer Engineering Igdır University, TurkeyFollow

Authors' ORCIDs

Takaaki Fujita: https://orcid.org/0000-0002-9380-386X

Ajoy Kanti Das: https://orcid.org/0000-0002-9326-1677

Suman Das: https://orcid.org/0000-0001-5682-9334

Sankar Prasad Mondal: https://orcid.org/0000-0003-4690-2598

Volkan Duran: https://orcid.org/0000-0003-0692-0265

Article Type

Research Article

Abstract

Finite hypergraphs generalize ordinary graphs by permitting each hyperedge to join any nonempty set of vertices, and thus provide a natural model for truly multiway interactions. To represent hierarchical and multi-layer structure, SuperHyperGraphs iterate the powerset operation so that set-valued entities created at one level can be treated as vertices at higher levels. Independently, recursive hypergraphs allow edge recursion: an edge may contain not only vertices but also lower-level edges, yielding nested (and possibly self-referential) incidence controlled by a specified recursion depth. In this work we introduce and axiomatize Recursive Neutrosophic SuperHyperGraphs, a unified framework that combines vertex hierarchy with edge recursion and equips incidences with neutrosophic degrees (truth, indeterminacy, and falsity) to capture graded and inconsistent information. The resulting model offers a flexible combinatorial language for complex systems whose higher-order relations are simultaneously nested and uncertain.

Keywords

Recursive SuperHyperGraph; Hypergraph; SuperHyperGraph; Recursive Hypergraph; Neutrosophic SuperHyperGraph

How to Cite

Fujita, Takaaki; Das, Ajoy Kanti; Das, Suman; Mondal, Sankar Prasad; and Duran, Volkan (2026) "Recursive Neutrosophic SuperHypergraphs with Illustrative Applications," Neutrosophic Systems with Applications: Vol. 26: Iss. 6, Article 5. DOI: https://doi.org/10.63689/2993-7159.1349