International Journal of Neutrosophic Science

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

Generalized of A-Closed Set and Ƈ- Closed Set in Fuzzy Neutrosophic Topological Spaces

Huda F. Khudair , Fatimah M. Mohammed

In this research paper, a new two classes of sets called fuzzy neutrosophic generalized A-closed sets and fuzzy neutrosophic generalized Ƈ-Closed sets in fuzzy neutrosophic topology are introduced and some of their properties have been investigated. We give some theorems, propositions and some necessary examples related to presented definitions. Then, we discuss the relations among the new defined sets.

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Vol. 19 Issue. 2 PP. 08-18, (2022)

Continuity and Compactness via Hypersoft Open Sets

Baravan A. Asaad , Sagvan Y. Musa

Hypersoft topology (HST) is the study of a structure based on all hypersoft (HS) sets on a given set of alternatives. In continuation of this concern, in this article, we introduce new maps namely HS continuous, HS open, HS closed, and HS homomorphism. We examine the main characteristics of each of these maps. Furthermore, we study HS compact space and discuss some of its properties. We point out that HS compactness preserved under HS continuous map.

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Vol. 19 Issue. 2 PP. 19-29, (2022)

Some Algebraic structures of Neutrosophic fuzzy sets

I. Silambarasan , R. Udhayakumar , Florentin Smarandache , Said Broumi

The mathematical operations of convergence, association, supplement, arithmetical total, logarithmic item, scalar increase, and exponentiation are the main topics of this article. We show certain important logarithmic features of idempotency, commutativity, associativity, retention, distributivity, and De Morgan’s laws over the addition of Neutrosophic fuzzy sets. We also outline new fixations and NFS widening and show some concepts in action. Last but not least, we define a further operation (@)on Neutrosophic fuzzy sets and investigate distributive laws for the case where the responsibilities of ⊕, ⊗, ∪, and ∩ are combined.

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Vol. 19 Issue. 2 PP. 30-41, (2022)

A Study on Plithogenic Fuzzy Relational Mapping and Its Application in Python Program

L.Jeromia Anthvanet , A. Rajkumar , D. Nagarajan , Broumi Said

In this research paper, we explore the notion of Plithogenic Fuzzy Relational Mapping (PFRM) and its applications. Plithogenic Fuzzy Relational Mapping concept is utilized as a logical procedure with a defined contradiction degree to evaluate multiple attributes. A Plithogenic fuzzy relational matrix is used as the adjacency matrix. Using Plithogenic fuzzy union and intersection operators, the resultant vector is calculated. The degree of contradiction for each attribute value with the dominating attribute gives a way to better accurate results. A case study has been taken and we have implemented the newly proposed idea. Python Program has been written using the algorithm proposed and we have obtained the result as well.

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Vol. 19 Issue. 2 PP. 42-56, ()

Neutrosophic approach to Dynamic Programming on group Decision Making problems

A. Kanchana , D.Nagarajan , Broumi Said

In this article, complicated group decision-making situations where the preference data is represented by linguistic variables are addressed using the dynamic programming approach. Making conclusions clear through accurate figures is difficult for decision-makers due to the complexity and ambiguity of reality. Neutrosophic is used to encode the linguistic variables because they cannot be directly computed. Neutrosophic sets are used to manage indeterminacy in a practical situation. The relationships between single and interval Neutrosophic sets are then measured using novel distance and similarity models. The suggested dynamic programming interval-based clustering methodology is then used to group the decision-makers. Additionally, a novel method for computing the interval weights of decision-makers and clusters is described, accounting for both the cluster center and group size. A centroid-based ranking system is then used to compare and order the possibilities, and illustrated experiments are presented to demonstrate how effectively the suggested technique operates. Comparisons and discussions are also done to show its superiority.

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Vol. 19 Issue. 2 PP. 57-65, (2022)

Nonagonal Neutrosophic Number and its Application in Optimization Technique

N. Jose Parvin Praveena , S. Ghousia Begum , A. Rajkumar , D. Nagarajan , Broumi Said

This article discusses Nonagonal Neutrosophic number and m-valued Nonagonal Neutrosophic number. The score function, the accuracy function, hamming distance, normalized hamming distance, Euclidean distance and normalized Euclidean distance of Nonagonal and m-polar Nonagonal Neutrosophic number are derived. Some de-neutrosophication method for Nonagonal Neutrosophic number and some properties of m-valued Nonagonal Neutrosophic number are proved. In this article the optimal path of an acyclic network is estimated using Neutrosophic α-cut  grade, Neutrosophic Euclidean grade technique and dynamic programming recursion method through Nonagonal Neutrosophic number. The score function and the removal area method are used to transform the Nonagonal Neutrosophic number to crisp number and the results obtained in both the methods are compared.

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Vol. 19 Issue. 2 PP. 66-79, (2022)

Applying Neutrosophic Iadov Technique for assessing an MDD-based approach to support software design

Nemury Silega , G. F. Castro Aguilar , I. A. Martillo Alcívar , K. M. Faggioni Colombo