Search

This study discusses the use of t-neutrosophic graphs to express and understand complex interactions. It also shows how these graphs might manage intricate relationships with a wide range of variables or scenario elements. Additionally, it offers fundamental t-neutrosophic graph operations and talks about concepts in these graphs such as homomorphism and isomorphism. Additionally, the study addresses how this approach may be applied in practical contexts to address circular economies and sustainability growth. Through the use of t-neutrosophic graphs, various components, and their connections, the research demonstrates that managing the several circular dimensions is feasible. financial system. This example shows how adaptable and practical t-neutrosophic graphs are as a tool for developing policies and making decisions about complicated social issues that involve some numbers principles. [ABSTRACT FROM AUTHOR]

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets, and their combinations have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. A neutrosophic set has the potential to be a general framework for uncertainty analysis in various spectra. On the other hand, the idea of Fermatean neutrosophic sets (FNSs) is the hybrid model of Fermatean fuzzy sets and neutrosophic sets, developed to enable the analytical management of ambiguous data from relatively typical real-world decision-making scenarios. In this work, we develop an algorithm to compare the Fermatean neutrosophic set and the neutrosophic set, Fermatean Neutrosophic Weighted Arithmetic Mean (FNWAM) and Fermatean Neutrosophic Weighted Geometric Mean (FNWGM) operators as an accuracy function in addition to the conventional aggregating operators are designed. Further, the CODAS technique for Multiple Attribute Group Decision Making (MAGDM) problems according to the defined operators is proposed. Additionally, to make a clear understanding of the presented study, a university faculty selection problem is studied to illustrate the proposed methodology. Finally, the results of the above two sets prove the authenticity of this study. [ABSTRACT FROM AUTHOR]

Graph theory plays a vital role in modeling real-world scenarios like network security and expert systems. Various extensions of graph theoretical conceptions have been designed for addressing uncertainty in graphical network scenarios. The concept of Fermatean Neutrosophic Dombi Fuzzy Graphs (FNDFgraphs) represents a novel and innovative extension in graph theory, combining the principles of Fermatean Neutrosophic fuzzy graphs and the Dombi operator. FNDFGs enhances the representation and analysis of uncertain rela- tionships in a graph also it offers a more comprehensive and exible approach to modeling uncertainty in graph structures. The main objective of this present research study focused on FNDFGs and their operations. At the end, an algorithm for Fermatean Neutrosophic Dombi fuzzy multi-criteria decision-making is given, which incorporate the concepts of Fermatean Neutrosophic sets and Dombi operations. Furthermore, a numerical example based on the selection of the most suitable CIBIL score application is put forward to illuminate the aptness of the proposed research work. [ABSTRACT FROM AUTHOR]

A neutrosophic set is a mathematical framework that extends fuzzy and intuitionistic sets to handle indeterminate or contradictory information using three components: truth, falsity, and indeterminacy -membership degrees which deal with handling indeterminate, imprecise, and uncertain data, while Extended Fuzzy Theory extends the standard fuzzy set theory to manage more intricate membership degrees. The primary objective of this review is to thoroughly investigate and summarize the existing literature on trapezoidal neutrosophic environments, particularly focusing on aspects such as the NFMOLP Problems in SVTpN environments. Ultimately, this comprehensive review article aims to enhance the understanding of the potential of these integrated methodologies for effectively presenting decision-making amidst complex and uncertain conditions. [ABSTRACT FROM AUTHOR]

The notion of Fuzzy Graphs (FGs) and Intuitionistic Fuzzy Graphs (IFGs) is generalized in the Picture Fuzzy Graph (PFG), which is a more common platform for expressing the degree of positive, negative, and neutral membership functions. Picture Fuzzy Soft Graphs (PFSGs) are powerful mathematical tools for modeling real-world vagueness. The concept of vulnerability parameters of PFSG is provided in this research work by introducing the novel cardinality, domination number, integrity, and Domination Integrity (ÐÏ) of PFSG. Furthermore, a decision-making method for the PFSG has been presented using ÐÏ to suggest an algorithm for determining the ideal location for establishing a city diagnosis center. [ABSTRACT FROM AUTHOR]

An L (p1, p2, p3, ... , pm)- labeling of a graph G, has the vertices of G assigned with non-negative integers, such that the vertices at distance j should have at least pj as their label difference. If m = 3 and p1 = 3, p2 = 2, p3 = 1, it is called an L (3, 2, 1)-labeling which is widely studied in the literature. In this paper, we define an L (3, 2, 1)-path coloring of G as a labeling g : V (G) → Z+ such that between every pair of vertices there exists at least one path P where in the labeling restricted to this path is an L (3, 2, 1)-labeling. Among the labels assigned to any vertex of G under g, the maximum label is called the span of g. The L (3, 2, 1)-connection number of a graph G, denoted by k3c (G) is defined as the minimum value of span of g taken over all such labelings g. We call graphs with the special property that k3c (G) = |V (G) | as L (3, 2, 1)-path graceful. In this paper, we obtain k3c (G) of graphs that possess a Hamiltonian path and carry forward the discussion to certain classes of graphs which do not possess a Hamiltonian path, which is novel to this paper. Although different kinds of labeling are studied in the literature with different mathematical constraints imposed, the idea of showing the existence of a graph with a given number as its minimum labeling number has rarely been addressed. We show that given any positive integer, there always exists an L (3, 2, 1)-path graceful graph with the given integer as its k3c (G), thus addressing the inverse question. Finally exploiting the fact that there is no gap on the k3c (G) number line, we give an application of path colorings for secure communication on social networking sites. Efforts to deploy graph coloring in task scheduling, interference-free transmission, etc have been dealt by earlier researchers. In this paper, we deploy the L (3, 2, 1)-path coloring technique defined by us for secure communication in social networks, which has not been dealt with so far. [ABSTRACT FROM AUTHOR]

The shortest path problem is a classic optimization problem in graph theory and computer technology. It involves identifying the shortest path between two nodes in a graph, where each edge has a numerical weight. In this paper, we put our effort into examining the use of the dynamic programming method to evaluate the shortest path (SP) between the two specified nodes in a multistage network where the parameter is a multi-value neutrosophic number (MVNN). Firstly, we propose an algorithm based on the forward and backward approach in an uncertain environment and also implement our approach in the Python-3 programming language. Furthermore, a numerical illustration has been provided to showcase the effectiveness and robustness of the novel model. [ABSTRACT FROM AUTHOR]

Business has a massive effect on both people and society as a whole in today's culture. Businesses make significant contributions to humanity's general well-being and progress by promoting economic growth, supporting innovation, producing wealth, and addressing social challenges. However, choosing the right location for a business is a complex task, involving multiple criteria and qualitative and quantitative factors that heavily rely on expert judgement. The researchers propose a unique approach called the SVNZN multi-attributed decision-making method to aid decision-makers in this process. They introduce new operating laws for SVNZNs based on the sine trigonometric (ST) function, known for its periodicity and symmetry over the origin, making it favorable for decision-makers over multi-time phase parameters. Additionally, novel AOs such as SVNZN weighted averaging and geometric operators are defined to combine SVNZNs effectively. Based on these AOs, a decision-making technique for MADM problems is presented, and its applicability is demonstrated through a numerical example of selecting the best location for a business. To validate and enhance the understanding of these proposed techniques, the researchers conducted a comprehensive comparison analysis, including a sensitivity analysis, considering existing literature on MADM difficulties. Figure 1 provides a thorough graphical summary by visually representing all of the contributions and outcomes. [ABSTRACT FROM AUTHOR]

The goal of this article is to establish a methodology for ordering of single-valued neutrosophic numbers (SVN-numbers) on the basis of values and ambiguities. First of all, the idea of neutrosophic numbers is discussed, and (α, β, γ)-cut and arithmetic oprations definecd over SVN-numbers are examined. Thereafter, corresponding to each components, the values and ambiguities are defined and using these definitions, the ratio ranking function is constructed. Then, for the stability of the ratio ranking function, some examples are provided for comparing this method with other approaches. Applying this ratio ranking function, neutrosophic linear programming problem(Neu-LPP) converts to the crisp linear programmning problems (CLP-Problems) and solved it by computational lingo method. At last, Neu-LPP is illustrated by two numerical real-life examples. [ABSTRACT FROM AUTHOR]

Efficiently determining optimal paths and calculating the least travel time within complex networks is of utmost importance in addressing transportation challenges. Several techniques have been developed to identify the most effective routes within graphs, with the Reversal Dijkstra algorithm serving as a notable variant of the classical Dijkstra's algorithm. To accommodate uncertainty within the Reversal Dijkstra algorithm, Fermatean neutrosophic numbers are harnessed. The travel time associated with the edges, which represents the connection between two nodes, can be described using fermatean neutrosophic numbers. Furthermore, the edge weights in fermatean neutrosophic graphs can be subject to temporal variations, meaning they can change over time. In this study, an extended version of the Reversal Dijkstra algorithm is employed to discover the shortest path and compute the minimum travel time within a single-source time-dependent network, where the edges are weighted using fermatean neutrosophic representations. The proposed method is exemplified, and the outcomes affirm the effectiveness of the expanded algorithm. The primary aim of this article is to serve as a reference for forthcoming shortest path algorithms designed for time-dependent fuzzy graphs. [ABSTRACT FROM AUTHOR]

Fractional transportation problem that includes source and destination may have fractional objective functions in real-world applications to maximize the profitability ratio like profit/cost or profit/time. We refere to such transportation problems as fractional transportation problem. The paper considers the interval-valued neutrosophic numbers and its aritemematic operations. This paper deals with fractional transportation problem having discounting cost in neutrosophic environment, where the supply, demand and transportation costs are uncertain. The problem is considered by introducing all the parameters as neutrosophic numbers. Using the benefits of the score function definition, the problem is transformed into the corresponding deterministic form which can be illustrated by any method. and hence by applying of least cost method with the help of Kuhn-Tucker' optimality conditions, the optimal solution is resulted. Our strategy is to assess the issue and can rank different sort of neutrosophic numbers. To claify the proposed technique, a numerical example is given to show the adequacy of the new model. [ABSTRACT FROM AUTHOR]