Neutrosophic Matrix Research Articles

Slope Stability Classification Model Based on Single-Valued Neutrosophic Matrix Energy and Its Application Under a Single-Valued Neutrosophic Matrix Scenario

Slope Stability Classification Model Based on Single-Valued Neutrosophic Matrix Energy and Its Application Under a Single-Valued Neutrosophic Matrix Scenario

MAGDM Model Using Single-Valued Neutrosophic Credibility Matrix Energy and Its Decision-Making Application

This paper aims to develop a MAGDM model using single-valued neutrosophic credibility matrix (SVNCM) energy in a SVNCM scenario. To do it, first, SVNCM energy and its score function are presented as a conceptual extension of existing single-valued neutrosophic matrix (SVNM) energy. Then, a MAGDM model is developed in terms of SVNCM energy and its score function in a SVNCM scenario and also its decision algorithm is provided to solve MAGDM problems with SVNCMs. Finally, the developed MAGDM model is applied in the school site selection problem as an actual example, then the comparative investigation of the decision results in the SVNM and SVNCM scenarios indicates the superiority of the developed model over existing MAGDM model.

The energy of multi-valued neutrosophic matrix and neutrosophic hesitant matrix and relationship between them in multi-criteria decision-making

The concept of energy in graphs and matrices is frequently used in all application fields. The energy of a matrix is an extended version of the energy of a graph. The neutrosophic matrix energy concept needs to be more noticeable in multi-criteria decision-making environments. This study presents the concept of the energy of a multi-valued neutrosophic matrix. The upper and lower bounds of the proposed energy were determined. The connection between the neutrosophic hesitant matrix and the multi-valued neutrosophic matrix is provided. Since the parameters of the two matrices differ in truth, indeterminacy, and false entries, the matrix is converted into a single-valued form, and then the energy was calculated. The MCDM problem was addressed with the proposed energy, which is solved by a novel decision-making method. The task is to select a machine from a group of repaired machines in a particular industry that is in good condition. The final ranking values are calculated by the ranking energy formula that decides which is preferred. Then the comparative results were given to demonstrate the accuracy of the proposed energy outcomes.

Application of multi-valued rough neutrosophic set and matrix in multi-criteria decision-making

Rough set concept is a methodology of information processing for relational databases. It is a unique uncertainty mathematics topic closely connected to fuzzy set theory. When the rough set is combined with neutrosophic set theory, an effective tool for working with indeterminacy arises. In this study, we defined a multi-valued rough neutrosophic set and a multi-valued rough neutrosophic matrix. Using separation measures, we introduced a new approach for a multi-valued neutrosophic with a rough structure. We consider the problem of determining the condition of dengue-affected patients in a specific hospital. Using this method, we create a multi-valued rough neutrosophic decision matrix that clearly displays the relationship between patient conditions and symptoms. We can determine which one has a serious condition by solving this problem and presenting it on the graph.

Linguistic neutrosophic matrix energy and its application in multiple criteria group decision-making

Matrix energy is an important representation tool of collective information. Then, it is not applied to various fuzzy and linguistic environments. To compensate for this gap, this article aims to extend the matrix energy to propose the energy of a linguistic neutrosophic matrix (LNM) for solving a multiple criteria group decision-making (MCGDM) problem, which fully contains LNMs of decision-maker weights, criteria weights, and alternative evaluations. To realize the objective, this study first presents the energy of LNM in view of the true matrix energy, the false matrix energy, and the indeterminate matrix energy. Then, a MCGDM technique is established in view of the LNM energy method in a LNM circumstance. Finally, the developed MCGDM technique using the LNM energy is used to solve the hospital location choice problem in the full LNM scenario. Meanwhile, the decision results indicate the validity and usability of the established MCGDM technique.

The energy of interval valued neutrosophic matrix in decision-making to select the manager for the company project

The concept of energy in graphs and matrices is used effectively in all application areas. The energy of the matrix is an extension of graph energy. The usage of the energy idea in neutrosophic matrices makes it more flexible and applicable in multi-criteria decision-making environments. In this paper, we propose the energy approach in neutrosophic matrices with interval values. We determined the given energy’s upper and lower bounds. The energy is used of the interval-valued neutrosophic matrix to address the MCDM problem. A new strategy has been introduced called the interval-valued neutrosophic energy method to solve this problem. We look at the problem of choosing a qualified manager for a business project. A team of professionals in the company evaluates the options using neutrosophic numbers with interval values, and the energy method is then used to calculate the result. The result has been compared with the TOPSIS method results to show that the outcomes are similar.

Some algebraic properties on rough neutrosophic matrix and its application to multi-criteria decision-making

<abstract><p>Rough set theory is a method of information processing for database systems. The neutrosophic matrix is a generalization of the fuzzy matrix, especially in handling indeterminacy situations. The concept of matrix theory and its energy in the neutrosophic environment help to determine the value of the uncertain matrix. In this paper, we correlate the rough set theory with the neutrosophic matrix theory to introduce the rough neutrosophic matrix (RNM). In this structure, lower and upper approximation neutrosophic matrices are used to deal with uncertain situations. We demonstrate that the given matrix plays a different role in decision-making situations and defined the proposed matrix's determinant, adjoint, algebraic properties and operations. Finally, derived the ranking function for a rough neutrosophic matrix's energy. The new multi-criteria decision-making (MCDM) approach was presented with the ranking formula, which was utilized to rank the alternatives, and numerical examples were provided to show how the proposed matrix and its energy could be applied to an MCDM problem.</p></abstract>

Determinant of a Neutrosophic Matrix

In this paper, we study some properties of the determinant of a neutrosophic matrix. Also, we prove that |A.adj(A)|=|A|=|adj(A).A| and define the matrices A_((p_1…p_m |q_1…q_m))and A_((p→q)). Further, a method is presented for calculating the determinant of a neutrosophic matrix that has a large number of columns and rows. KEYWORDS adjoint, identity neutrosophic matrix, permutation, principal submatrix, transpose, triangular NM

The Energy of rough neutrosophic matrix and its application to MCDM problem for selecting the best building construction site

An approach to data processing for relational databases is called a rough set theory. It is an interesting area of uncertainty mathematics that is mainly related to fuzzy theory. Rough set theory and neutrosophic set theory can be joined to create a powerful tool for dealing with indeterminacy. Neutrosophic matrices help decision-makers deal with multi-criteria decision-making by providing them with more useful and practical when we apply the concept of matrix energy. In this paper, we defined a Rough neutrosophic matrix and its energy. Some propositions, lower and upper limits of the rough neutrosophic matrix's energy were derived. The proposed energy of the rough neutrosophic matrix was applied in multi-criteria decision-making problems. The problem is to select the best place for constructing the school building. Applying the energy method to the MCDM problem became more relatable and produced good results.

Interval neutrosophic matrix game-based approach to counter cybersecurity issue

Interval neutrosophic matrix game-based approach to counter cybersecurity issue

On the Neutrosophic Characteristic Polynomials and Neutrosophic Cayley-Hamilton Theorem

The objective of this paper is to study some novel algebraic properties of neutrosophic matrices. Also, this work introduces the concept of neutrosophic characteristic polynomial of a square neutrosophic matrix and the neutrosophic version of Cayley-Hamilton. On the other hand, we illustrate many examples about the validity of this work.

On Some Novel Results About Neutrosophic Square Complex Matrices

The objective of this paper is to study algebraic properties of complex neutrosophic matrices, where a necessary and sufficient condition for the invertibility of a complex square neutrosophic matrix is presented by defining the complex neutrosophic determinant. On the other hand, this work introduces the concept of neutrosophic characteristic polynomial and neutrosophic Cayley-Hamilton theorem for the complex case.

On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems

This work is dedicated to classifying the general n-refined neutrosophic ring by building a ring isomorphism and the direct product of the corresponding classical rings with itself. On the other hand, we use the classification property to solve the problem of n-refined neutrosophic computing of Eigen values and Eigen vectors of an n-refined neutrosophic matrix. Also, it will be applied to solve n-refined linear systems and models.

Complex Neutrosophic Matrix with Some Algebraic Operations and Matrix Norm Convergence

Complex Neutrosophic Matrix with Some Algebraic Operations and Matrix Norm Convergence

Neutrosophic Matrix Games to Solve Project Management Conflicts

A project is an effort made by a group of actors during a certain period to obtain a product, service, or result. Project management is the application of knowledge, skills, tools, and techniques to plan and execute activities to achieve the project requirements. Project management implies the need for negotiation between the parties because there may be a contradiction between the parties involved, that is, e.g. between the one who provides the knowledge or goods and the client who receives the final product or knowledge. That is why we propose a neutrosophic solution to manage the contradictions in the negotiation and execution of any project. The advantages offered by this solution are that the data can be entered in the form of linguistic terms, in addition to explicitly including the indeterminacy that exists in the modeling of this type of activity. This methodology is useful in negotiating qualitative content between parties.

On the Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations

The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.

A Review On Some Neutrosophic Algebraic Linear Structures

This paper is dedicated to reviewing some of the basic concepts in neutrosophic linear algebra and its generalizations, especially neutrosophic vector spaces, refined neutrosophic, and n-refined neutrosophic vector spaces. Also, this work gives the interested reader a strong background in the study of neutrosophic matrix theory and n-refined neutrosophic matrix theory. We study elementary properties of these concepts such as Kernel, AH-Quotient, and dimension.

Plithogenic Cognitive Maps in Decision Making

Plithogenic sets introduced by Smarandache (2018) have disclosed new research vistas and this paper introduces the novel concept of plithogenic cognitive maps (PCM) and its applications in decision making. The new approach of defining instantaneous state neutrosophic vector with the confinement of indeterminacy to (0,1] is proposed to quantify the degree of indeterminacy. The resultant vector is obtained by applying instantaneous state vector through the connection matrix together with plithogenic operators comprising the contradiction degrees. The connection matrix is represented as fuzzy matrix and neutrosophic matrix and the resultant vector is determined by applying plithogenic fuzzy operators and plithogenic neutrosophic operators respectively. The obtained results are highly feasible in making the decision as it incorporates the contradiction degree of the conceptual nodes with respect to the dominant node. This research work will certainly pave the way for developing new approaches in decision making using PCM.

SINGLE VALUED (2N+1) SIDED POLYGONAL NEUTROSOPHIC NUMBERS AND SINGLE VALUED (2N) SIDED POLYGONAL NEUTROSOPHIC NUMBERS

This paper introduces a single valued (2n as well as 2n+1) sided polygonal neutrosophic numbers in continuation with other defined single valued neutrosophic numbers. The paper provides basic algebra like addition, subtraction and multiplication of a single valued (2n as well as 2n+1) sided polygonal neutrosophic numbers with examples. In addition, the paper introduces matrix for single valued (2n as well as 2n+1) sided polygonal neutrosophic matrix and its properties

Complex neutrosophic concept lattice and its applications to air quality analysis

In the current year, the precise measurement of uncertainty and fluctuation exists in a complex fuzzy attributes is addressed as computationally and mathematically expensive tasks with regard to its graphical analytics. To deal with this problem the calculus of complex neutrosophic sets are recently introduced to characterize the uncertainty and its changes based on its truth, indeterminacy, and falsity membership–value, independently. This given a way to represent the given data sets in form of complex neutrosophic matrix for further analysis towards knowledge processing tasks. In this process, a major problem arises when an expert wants to find some of the interesting patterns in the given complex neutrosophic data sets to solve the particular problem. To resolve this issue, the current paper proposes a method for step by step demonstration to investigate the complex neutrosophic concepts and their graphical structure visualization based on their Lower Neighbors. One of the suitable examples of the proposed method is also given for precise measurement of uncertainty exists in Air Quality Index (AQI) and its pattern at given phase of time.