Exploring Concepts of HyperFuzzy, HyperNeutrosophic, and HyperPlithogenic Sets (II)
Takaaki Fujita · Florentin Smarandache
Jan 2025 · Infinite Study
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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 a nalyzes t heir m athematical properties.
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