Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Article
Publication Date
2025
Abstract
This paper delves into the advancements of classical set theory to address the complexities and uncertainties inherent in real-world phenomena. It highlights three major extensions of traditional set theory - Fuzzy Sets [288], Neutrosophic Sets [237], and Plithogenic Sets [243] - and examines their further generalizations into Hyperfuzzy [106], HyperNeutrosophic [90], and Hyperplithogenic Sets [90]. Building on previous research [83], this study explores the potential applications of HyperNeutrosophic Sets and SuperHyperNeutrosophic Sets across various domains. Specifically, it extends f undamental c oncepts such as Neutrosophic Logic, Cognitive Maps, Graph Neural Networks, Classifiers, and Triplet Groups through these advanced set structures and briefly analyzes their mathematical properties.
Publication Title
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
Volume
4
First Page
91
Last Page
151
Language (ISO)
English
Keywords
Fuzzy set, Neutrosophic set, Hyperstructure, Hyperfuzzy set, Hyperneutrosophic set.
Recommended Citation
Fujita, Takaaki and Florentin Smarandache.
"Exploring Concepts of HyperFuzzy, HyperNeutrosophic, and HyperPlithogenic Sets (II)."
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.
