Hesitant Neutrosophic Network Models for Operations Research: Graphs, Hypergraphs, and Superhypergraphs

Takaaki Fujita

doi:10.64060/ANMIV1i23

Authors

Takaaki Fujita Independent Researcher, Tokyo, Japan Author

DOI:

https://doi.org/10.64060/ANMIV1i23

Keywords:

Superhypergraph, Hypergraph, Hesitant Neutrosophic Graph, Hesitant Neutrosophic HyperGraph, Hesitant Neutrosophic SuperHyperGraph

Abstract

Graphs provide a standard language for representing connectivity via vertices and pairwise edges, yet many real interactions are genuinely higher–order. Hypergraphs capture such multiway relations by allowing each hyperedge to join an arbitrary nonempty vertex subset. To further model nested and hierarchical incidence, SuperHyperGraphs iterate the powerset construction over a finite base set, so that vertices may become set-valued objects across multiple levels. Motivated by uncertainty in modern relational data, we study hesitant neutrosophic sets, in which each element is described by a finite family of admissible truth–indeterminacy–falsity triples. This framework contains hesitant fuzzy sets and single-valued neutrosophic sets as special cases. We then transfer these semantics to network structures by introducing hesitant neutrosophic graphs and extending them to hesitant neutrosophic hypergraphs and hesitant neutrosophic superhypergraphs. The resulting hierarchy offers a unified formalism for representing uncertainty in pairwise, multiway, and multi-level relational systems.

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