Download or read book Exploring Concepts of HyperFuzzy, HyperNeutrosophic, and HyperPlithogenic Sets (I) written by Takaaki Fujita and published by Infinite Study. This book was released on 2025-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.