Some Types Of Hyperneutrosophic Set 5 Support Paraconsistent Faillibilist And Others


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Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others


Some Types of HyperNeutrosophic Set (5): Support, Paraconsistent, Faillibilist, and Others

Author: Takaaki Fujita

language: en

Publisher: Infinite Study

Release Date: 2025-01-01


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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.

Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined


Some Types of HyperNeutrosophic Set (7): Type-m, Nonstationary, Subset-valued, and Complex Refined

Author: Takaaki Fujita

language: en

Publisher: Infinite Study

Release Date: 2025-01-01


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This paper builds upon the foundational advancements introduced in [26,39–43]. TheNeutrosophic Set provides a versatile mathematical framework for addressing uncertainty through its three membership functions: truth, indeterminacy, and falsity [84]. Extensions such as the Hyperneutrosophic Set and the SuperHyperneutrosophic Set have been recently proposed to address increasingly complex and multidimensional problems. Detailed formal definitions of these concepts can be found in [33]. In this paper, we extend the Type-𝑚, Nonstationary, Subset-Valued, and Complex Refined Neutrosophic Sets using the Hyperneutrosophic Set and the SuperHyperneutrosophic Set frameworks.

Some Types of HyperNeutrosophic Set (6): MultiNeutrosophic Set and Refined Neutrosophic Set


Some Types of HyperNeutrosophic Set (6): MultiNeutrosophic Set and Refined Neutrosophic Set

Author: Takaaki Fujita

language: en

Publisher: Infinite Study

Release Date: 2025-01-01


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This paper builds on the foundational advancements introduced in [22, 29–32]. The Neutrosophic Set pro-vides a flexible mathematical framework for managing uncertainty by utilizing three membership functions: truth, indeterminacy, and falsity. Recent extensions, such as the HyperNeutrosophic Set and the SuperHy-perNeutrosophic Set, have been developed to address increasingly complex and multidimensional challenges. Comprehensive formal definitions of these concepts are provided in [26]. In this paper, we further extend various specialized classes of Neutrosophic Sets. Specifically, we explore extensions of the MultiNeutrosophic Set and the Refined Neutrosophic Set using HyperNeutrosophic Sets and 𝑛-SuperHyperNeutrosophic Sets, providing detailed analysis and examples.