International Journal of Neutrosophic Science

Herein, we further contribute and promote topological structures via bipolar hypersoft (BHS) setting by introducing new types of maps called BHS continuous, BHS open, BHS closed, and BHS homeomorphism maps. We investigate their characterizations and establish their main properties. By providing a thorough picture of the proposed maps, we investigate the concept of BHS compact space and obtain several results relating to this concept. We point out that BH compactness preserved under BH continuous map. The relationships among these concepts with their counterparts in hypersoft (HS) structures are discussed.

The fuzzy graph theory uses a substantial and important role in modelling and structuring many optimization problems. DIfferent type of uncertainties exist in most of the optimization problems in real lIfe scenarios due to indeterminate and incomplete information and it is a challenging task for the expert to design those optimization problems applying fuzzy graph. To design the incomplete, uncertainty and vagueness in graphical optimization problems, several extensions of graph theoretical ideas are proposed. The idea of neutrosophic graph plays an important role to manage the uncertainty, linked with the indeterminate and incomplete data/information of any optimization problem. In this manuscript, we present the idea of regular neutrosophic graph, strong neutrosophic graph, bipartite neutrosophic graph, regular neutrosophic graph, and regular strong neutrosophic graph. We also introduce six different operations on neutrosophic graph, viz., cartesian product, composition, join, direct product, lexicographic and strong product.

Performing a correct architectural design is essential to satisfy the quality requirements of a software. In this phase, the high-level components that will compose the system, as well as their relationships, are defined. Since the architects must struggle with complex and challenging tasks in this phase, providing them with advanced and helpful tools and methods is suitable. For example, MDD-based approaches are a valuable means to deal with the complexity during the software development process, particularly during the architectural design stage. However, despite the notable benefits of this type of approaches, the architects are often sceptical about adopting new technologies. Hence, before formally adopting new methods or tools, it is suitable to consider the opinion of those using them. In that sense, this paper aims to describe the results of an assessment of an MDA-based approach to support the architectural design. This assessment was carried out applying the Iadov neutrosophic technique. This technique has been extensively applied in a wide variety of domains to analyze the satisfaction level of potential users of different proposals. The results indicate a high satisfaction level of potential users of the assessed approach.

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.

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.

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.

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.

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.

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.