Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined

Authors

Takaaki Fujita
Florentin Smarandache, University of New MexicoFollow

Document Type

Article

Publication Date

2025

Abstract

This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.

Publication Title

Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond

Volume

4

First Page

233

Last Page

248

Language (ISO)

English

Keywords

Set Theory, SuperhyperNeutrosophic set, Neutrosophic Set, HyperNeutrosophic set.

Recommended Citation

Fujita, Takaaki and Florentin Smarandache. "Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined." Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond , (2025): 233-248. https://digitalrepository.unm.edu/math_fsp/771

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.