The theory of plithogeny developed by Smarandache is described as a more generalized form of representing sets of different nature such as crisp, fuzzy, intuitionistic and neutrosophic. Plithogenic set comprises degree of appurtenance and contradiction degree with respect only to the dominant attribute. This paper introduces extended plithogenic sets comprising degrees of appurtenance and contradiction with respect to both dominant and recessive attributes. The extension of the 5-tuple Plithogenic sets to a 7- tuple plithogenic sets helps in developing a more comprehensive kind of Plithogenic sociogram. The newly developed plithogenic sets and its implications in Plithogenic sociogram is validated by the decision making problem on food processing industries. The obtained results using extended plithogenic sets are more promising in comparison to the conventional plithogenic sets. The proposed kind of plithogenic sets will benefit the decision makers to make optimal decisions based on both optimistic and pessimistic approaches.
Read MoreDoi: https://doi.org/10.54216/IJNS.200401
Vol. 20 Issue. 4 PP. 08-35, (2023)
A new classes of sets called fuzzy neutrosophic M-open sets and fuzzy neutrosophic M-Closed sets in fuzzy neutrosophic topology are introduced some characterizations of these notions have been presented. After given the fundamental definitions of the new notions, we studided some theorems, propositions and some necessary relations with examples related to these notions had been discussed.
Read MoreDoi: https://doi.org/10.54216/IJNS.200402
Vol. 20 Issue. 4 PP. 36-45, (2023)
In this paper, we introduce the notion of non- Archimedean neutrosophic normed space and also establish Hyers-Ulam-Rassias-type stability results concerning the Cauchy, Pexiderized Cauchy. We determine some stability results concerning the Cauchy, Jensen and its Pexiderized functional equations in the framework of non-Archimedean Neutrosophic Normed Space. This work indeed presents a relationship between four various disciplines, the theory of neutrosophic normed space, non – Archimedean, Hyers-Ulam-Rassias stability and functional equation.
Read MoreDoi: https://doi.org/10.54216/IJNS.200403
Vol. 20 Issue. 4 PP. 46-57, (2023)
This is a review paper, where we recall the definitions together with practical applications of the Soft Set and its extensions to HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set.
Read MoreDoi: https://doi.org/10.54216/IJNS.200404
Vol. 20 Issue. 4 PP. 58-64, (2023)
Smarandache developed the idea of hypersoft set (HSS) theory as an extension of soft set (SS) theory. HSS provides a general mathematical framework for handling data that can be formulated as several trait-valued disjoint sets which blend to various traits. The major goal of this article is to lay the footing for supplying a new model called bipolar fuzzy hypersoft sets (BFHSSs) by linking both fuzzy sets (FSs) and HSSs under bipolarity property. By using positive and negative membership functions and multi-argument functions, these structures work best for testing uncertainty. This makes them better at solving real-world problems, especially ones that have both good and bad sides. This paper also has different operations for BFHSSs, such as absolute BFHSS, null BFHSS, complement, subset, union, intersection, and their related properties. Moreover, operations like OR and AND for BFHSS have been instituted. Some properties are demonstrated, and some numerical examples are given to illustrate the mechanism of using these tools. Finally, these tools are applied in the decision-making process based on an algorithm that is built.
Read MoreDoi: https://doi.org/10.54216/IJNS.200405
Vol. 20 Issue. 4 PP. 65-77, (2023)