International Journal of Neutrosophic Science

In the final years of the 20th century, the notion of generalized topological spaces was introduced, marking a significant shift in the field of topology. This paper focuses on a subset of ℘(X) on a non-empty set X that is closed under arbitrary unions, defining a generalized topology and subsequently a generalized topological space (GTS) denoted by (X,μ). Within this framework, we explore the concept of Noetherian generalized topological spaces and delve into the properties of μ-L-closed subsets within the Noetherian GTS. The investigation reveals that subspaces of a μ-Noetherian GTS X, with the induced topology, inherit the μ-Noetherian property and exhibit finitely many non-empty μ-irreducible components. Furthermore, the study extends to the analysis of hereditary properties, regular 〖μ-G〗_δ, 〖μ-d〗_δ, μ-irreducible L-closed subsets, and the product properties of μ-L-closed subsets under (μ,μ')-continuous functions. We also establish the closure property of finite unions in μ-Noetherian GTS and clarify the homeomorphic nature of μ-Noetherian GTS (X,μ)  to itself.

Multi-criteria decision-making (MCDM), which has been called a revolution in the field, is one of the most exact methods for making decisions. Multicriteria decision-making (MCDM) is the process of selecting options by considering multiple criteria to determine which is best. A multitude of applications in engineering, design, and finance are possible with the tools and methods derived from MCDM. Application-oriented problems with multiple criteria involve ambiguous and more inaccurate options, to deal with this ambiguity Smarandache introduced Treesoft sets, which are an extension of hypersoft sets. So, in this paper, we will consider a real-life application-oriented problem “Desalination process” under the treesoft sets environment and find the best method for desalination using one of the MCDM methods.

In this study, we introduce the concepts of MBJ-Neutrosophic WI-ideal and MBJ-Neutrosophic lattice ideal of lattice Wajsberg algebras. We demonstrate that every MBJ-Neutrosophic WI-ideal of lattice Wajsberg algebra is an MBJ-Neutrosophic lattice ideal of lattice Wajsberg algebra. Additionally, we talk about its opposite. Furthermore, we discover that in lattice H-Wajsberg algebra, every MBJ-Neutrosophic lattice ideal is an MBJ-Neutrosophic WI-ideal.

This article examines Pythagorean neurosophic vague set (PyNVS) problems relevant to multiple attribute decision-making (MADM). Pythagorean vague set (PyVS) and neutrosophic set (NS) can be generalized into Pythagorean neutrosophic vague set (PyNVS). We discuss log Pythagorean neutrosophic vague weighted averaging (log PyNVWA), logarithmic Pythagorean neutrosophic vague weighted geometric (log PyNVWG), log generalized Pythagorean neurosophic vague weighted averaging (log GPyNVWA) and log generalized Pythagorean neutrosophic vague weighted geometric (log GPyNVWG). In this article, we define the Euclidean distance (ED), Hamming distance (HD), operator laws, and flowchart using an algorithm. By analyzing log PyNVS through algebraic operations, we discuss its properties. They can identify the best option more quickly and understand the practicalities better. An illustrative example of this is the fusion of computer science and machine tool technology in agriculture. Furthermore, there are autonomous robot tractors and soil sterilization robots that can harvest crops, weed, and take photos of seed planting with seedlings. A random selection of five farmers (alternatives) has been made. Climate, water, soil, disease, and flooding are all criteria to consider when choosing a farmer. Our goal is to narrow down the options by comparing expert judgments with the criteria.

The incorporation of expert opinions and handling of data uncertainty are addressed by Al-Alkhazaleh through the introduction of a soft expert set. This extension of the soft set framework aims to enhance the analysis and decision-making processes by incorporating expert knowledge. On the other hand, the utilization of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) has been introduced as models to effectively handle uncertain data. In this work, the authors propose a model that combines the essential characteristics of fuzzy sets (FSs) and single neutrosophic sets (SVNSs) within expert systems. Consequently, this model aims to offer decision-makers increased flexibility when interpreting uncertain information, empowering them in the decision-making process. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given an aggregation operator (AO) for SVNFSESs to construct a new algorithm to demonstrate the method’s effectiveness in handling some real-life applications.

This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for the existence of the optimal solution to a BLP problem. Using the suggested methodology, the problem is formulated as a single-objective non-linear programming problem with several variables and constraints. Two typical numerical examples are examined to illustrate the proposed approach.

This study explores an innovative perspective on neutrosophic cubic Z-algebras, delving into the theoretical framework within mathematical structures. Through a comprehensive analysis, we uncover unique insights that contribute to the advancement of algebraic methodologies, particularly in handling uncertainties represented by neutrosophic elements. This work aims to present the idea of neutrosophic cubic sets in Z-algebras, as well as the usage of false membership function, truth, and indeterminacy in Z-algebras. Further, the results on -union, -intersection, -union, and -intersection of neutrosophic cubic Z-subalgebras are provided. This paper also discusses homomorphisms of Z-algebras and its associated characteristics.

This paper is dedicated to study the algebraic structures that are related to symbolic 16-plithogenic/17-plithogenic with symbolic plithogenic real entries, where symbolic 16-plithogenic/17-plithogenic eigenvectors and values will be discussed and presented in terms of theorems. As well as, the computation of determinants, inverses, and eigenvalues and vectors.

The goal of this paper is to classify and application of Physical Education (PE). PE growth rapidly these days due to rapid development in information technology. This rapid turn over the sports, training and physical education. So, this paper identifies the application of PE by using the Multi-Criteria Decision Making (MCDM) concept. This problem contains many criteria and sub-criteria. This paper proposed the Analytic Hierarchy Process (AHP) to determine the weights of criteria and sub-criteria. The AHP method was used under a neutrosophic environment to deal with uncertainty in this problem. An example is provided to show the outcomes of the proposed method.

In our work, we introduced a distinct subclass of univalent harmonic functions referred to as a subclass of chiral functions. These functions are defined by combining the generalized Komatu operator with the integral operator (R − K), which has positive coefficients within the unit disc A. Also, we generalize the same subclass into neutrosophic complex numbers. Throughout our investigation, we establish several properties associated with these functions, including coefficient estimates, the convex formula, the integral operator, and the Hadamard product. On the other hand, we present the Neutrosophic convex formula and the neutrosophic integral operator.

Almost all situations that arise in applied mathematics involve uncertainty, inconsistency, and indeterminacy. This can be simultaneously handled by the use of single valued neutrosophic fuzzy sets and single valued neutrosophic fuzzy numbers. In this paper, we propose the operations of addition, subtraction, and scalar  multiplication on trapezoidal single valued neutrosophic fuzzy numbers. We introduce some component-wise interval operations on the union of closed bounded intervals. Then we show how this can be used to perform the proposed operations on trapezoidal single valued neutrosophic fuzzy numbers with the help of finite α− cuts, finite β− cuts, finite γ− cuts, and finite δ− cuts, which we define in this paper itself.

We introduce the concept of new type of Diophantine neutrosophic set. A Diophatine neutrosophic set is the new type of a neutrosophic set and Diophatine fuzzy set (DioFS). We discuss Diophantine neutrosophic weighted averaging (DioNWA), Diophantine neutrosophic weighted geometric (DioNWG), generalized Diophantine neutrosophic weighted averaging(GDioNWA), generalized Diophantine neutrosophic weighted geometric (GDioNWG). In this article, we define the Euclidean distance (ED), Hamming distance (HD) and operator laws. By analyzing new type of Diophantine neutrosophic set through algebraic operations, we discuss its properties.

In this paper, we introduce the Single-Valued Neutrosophic Fuzzy Matrix (SVNFM), which consists of entries that are all single-valued neutrosophic fuzzy sets (SVNFS). Our objective is to provide a practical tool for dealing with uncertain and indeterminate input. To achieve this, we first define a neutrosophic fuzzy matrix (NFM) and discuss its fundamental properties. The use of various operations in decision making is a notable characteristic of single-valued neutrosophic fuzzy matrices (SVNFMs). In this paper, we propose a multicriteria group decision-making method that incorporates novel operations on neutrosophic fuzzy matrices. Finally, we present a case study to demonstrate the effectiveness of the proposed strategy.