International Journal of Neutrosophic Science

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Applications of Extended Plithogenic Sets in Plithogenic Sociogram

S.Sudha , Nivetha Martin , Florentin Smarandache

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.

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Vol. 20 Issue. 4 PP. 08-35, (2023)

An Introduction to M-Open Sets in Fuzzy Neutrosophic Topological Spaces

Zahraa A. Khalaf , Fatimah M. Mohammed

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.

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Vol. 20 Issue. 4 PP. 36-45, (2023)

Hyers - Ulam - Rassias Stability of Various Functional Equations in Non-Archimedean Neutrosophic Normed Spaces

R. Muthuraj , K. Nachammal , M. Jeyaraman

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.

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Vol. 20 Issue. 4 PP. 46-57, (2023)

New Types of Soft Sets: HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, and TreeSoft Set

Florentin Smarandache

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.

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Vol. 20 Issue. 4 PP. 58-64, (2023)

Bipolar fuzzy hypersoft set and its application in decision making

Ashraf Al-Quran , Faisal Al-Sharqi , Kifayat Ullah , Mamika Ujianita Romdhini , Marwa Balti , Mohammed Alomair

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.

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Vol. 20 Issue. 4 PP. 65-77, (2023)

A novel extension of hesitant fuzzy sets on UP (BCC)-algebras: neutrosophic hesitant fuzzy sets

Aiyared Iampan , S. Yamunadevi , P. Maragatha Meenakshi , N. Rajesh

In this paper, we introduce the concepts of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals of UP (BCC)-algebras. The characteristic neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals have also been studied. The relationshipbetween neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals and their level subsets is provided. The Cartesian product of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals is also supplied. Finally, we also find the property of the homomorphic pre-image of neutrosophic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and strong UP (BCC)-ideals.

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Vol. 20 Issue. 4 PP. 78-92, (2023)

δ-open sets in Neutrosophic Hypersoft Topological Spaces

P. Surendra , K. Chitirakala , A. Vadivel