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Full-Text Articles in Set Theory
Symbolic Hyperplithogenic Set, Takaaki Fujita, Florentin Smarandache
Symbolic Hyperplithogenic Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets, Neutrosophic Sets, and Plithogenic Sets have been widely investigated for tackling uncertainty, with numerous applications explored across various domains. As extensions of the Plithogenic Set, the HyperPlithogenic Set and the SuperHyperPlithogenic Set are also recognized. A Symbolic Plithogenic Set (SPS) is a structured set defined by symbolic components 𝑃𝑖 and coefficients 𝑎𝑖 , enabling flexible algebraic operations under a specified prevalence order. In this paper, we examine concepts including the Symbolic HyperPlithogenic Set and the Symbolic 𝑛-SuperhyperPlithogenic Set.
Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache
Plithogenic Duplets And Plithogenic Triplets, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
A Neutrosophic Set is a mathematical framework that represents degrees of truth, indeterminacy, and falsehood to address uncertainty in membership values [41, 42]. In contrast, a Plithogenic Set extends this concept by incorporating attributes, their possible values, and the corresponding degrees of appurtenance and contradiction [50]. Among the related concepts of Neutrosophic Sets, Neutrosophic Duplets and Neutrosophic Triplets are well-known. This paper defines Plithogenic Duplets and Plithogenic Triplets as extensions of these concepts using the Plithogenic Set framework and briefly examines their relationship with existing concepts.
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Hyperplithogenic Cubic Set And Superhyperplithogenic Cubic Set, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
Concepts such as Fuzzy Sets [23, 47], Neutrosophic Sets [32, 33], and Plithogenic Sets [35] have been extensively studied for addressing uncertainty, with diverse applications across numerous fields. Building on the Plithogenic Set, the HyperPlithogenic Set and SuperHyperPlithogenic Set have also gained recognition [15]. A Plithogenic Cubic Set integrates interval-valued and single-valued fuzzy memberships, augmented by multiattribute aggregation using plithogenic structures. This paper defines the HyperPlithogenic Cubic Set and SuperHyperPlithogenic Cubic Set and explores related concepts such as the HyperPlithogenic Fuzzy Cubic Set, HyperPlithogenic Intuitionistic Fuzzy Cubic Set, and HyperPlithogenic Neutrosophic Cubic Set.
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache
Plithogenic Superhypersoft Set And Plithogenic Forest Superhypersoft Set, Takaaki Fujita, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.