Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Article
Publication Date
2025
Abstract
This paper builds upon the foundational advancements introduced in [14, 25–27]. The Neutrosophic Set offers a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to tackle increasingly sophisticated and multidimensional problems. Detailed formal definitions of these concepts can be found in [20]. In this paper, we extend various specialized classes of Neutrosophic Sets—namely, the Support Neutrosophic Set, Neutrosophic Intuitionistic Set (distinct from the Intuitionistic Fuzzy Set), Neutrosophic Paraconsistent Set, Neutrosophic Faillibilist Set, Neutrosophic Paradoxist Set, Neutrosophic Pseudo-Paradoxist Set, Neutrosophic Tautological Set, Neutrosophic Nihilist Set, Neutrosophic Dialetheist Set, and Neutrosophic Trivialist Set—by utilizing the frameworks of the Hyperneutrosophic Set and the SuperHyperneutrosophic Set.
Publication Title
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
Volume
4
First Page
209
Last Page
220
Language (ISO)
English
Keywords
Set Theory, SuperhyperNeutrosophic set, Neutrosophic Set, HyperNeutrosophic set.
Recommended Citation
Fujita, Takaaki and Florentin Smarandache.
"Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others."
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
