Branch Mathematics and Statistics Faculty and Staff Publications
Document Type
Article
Publication Date
2025
Abstract
This work investigates the evolution of traditional set theory to address complex and ambiguous real-world phenomena. It introduces hierarchical hyperstructures and superhyperstructures, where superhyperstructures are formed by iteratively applying power sets to create nested abstractions. The focus is placed on three foundational set-based frameworks—Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets and their extensions into Hyperfuzzy Sets, HyperNeutrosophic Sets, and Hyperplithogenic Sets. These extensions are applied to various domains, including Statistics, TOPSIS, K-means Clustering, Evolutionary Theory, Topological Spaces, Decision Making, Probability, and Language Theory. By exploring these generalized forms, this paper seeks to guide and inspire further research and development in this rapidly expanding field.
Publication Title
Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond
Volume
4
First Page
11
Last Page
90
Language (ISO)
English
Keywords
Fuzzy set, Neutrosophic set, HyperStructure, HyperFuzzy set, HyperNeutrosophic set.
Recommended Citation
Smarandache, Florentin and Takaaki Fujita.
"Exploring Concepts of HyperFuzzy, HyperNeutrosophic, and HyperPlithogenic Sets (I)."
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.
