This analysis extends cylindrical and spherical frameworks within hyperneutrosophic sets, highlighting intricacies. It aims to deepen our understanding of multi-layered systems under uncertainty.
A Hyperstructure builds on the powerset idea to describe how elements of a set interact. Extending this notion, a Superhyperstructure employs higher-order powersets to represent hierarchical, multi-layer systems, enabling richer abstractions and more intricate relationships . A Neutrosophic Set models uncertainty using three membership aspects—truth, indeterminacy, and falsity—as introduced. These sets naturally generalize to HyperNeutrosophic Sets and to SuperHyperNeutrosophic Sets, which are defined within hyperstructural and superhyperstructural frameworks. In this paper, we extend Cylindrical, Spherical, HyperSpherical, and Triple-valued Neutrosophic Sets into the settings of Hyper- Neutrosophic Sets and SuperHyperNeutrosophic Sets. Throughout, the term SuperHyperNeutrosophic Sets specifically refers to the family of (m, n)-SuperHyperNeutrosophic Sets.
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Takaaki Fujita (2025) studied this question.
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