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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]

In this paper, a maple code is presented to do many operations on interval valued neutrosophic matrices including entering the elements of the matrix, checking whether a given matrix is an interval valued neutrosophic matrix or not, finding complement of an interval valued neutrosophic matrix, finding score, accuracy, and certainty measures, union and intersection of two interval valued neutrosophic matrices, sum and product of two interval valued neutrosophic matrices and finding the transpose of a given interval valued of neutrosophic matrix. What distinguishes this code is its simplicity to understand and to call the functions. Many examples are presented and solved successfully. [ABSTRACT FROM AUTHOR]

This paper aims to define a special case of neutrosophic matrices referred to as Fermatean neutrosophic matrices (FNMs). FNMs were introduced as generalization of Fermatean fuzzy matrices, intuitionistic fuzzy matrices, and Pythagorean neutrosophic matrices. In FNMs, some properties were discussed in connection with the well-known standard operations (⊕, ⊗, ∧ and ∨). In addition, the scalar multiplication (nA) and exponentiation ( An ) of a Fermatean neutrosophic matrix A were proposed, and their basic properties were investigated. Lastly, a new operation denoted by @ was defined on Fermatean neutrosophic matrices, and some of the properties of these matrices were examined. [ABSTRACT FROM AUTHOR]

The Neutrosophic Set (N s e t) represents the uncertainty in data with fuzzy attributes beyond true and false values independently. The problem arises when the summation of true (T r) , false (F a) , and indeterminacy I n values crosses the membership value of one, that is, T r + I n + F a < 1 . It becomes more crucial during decision-making processes like medical diagnoses or any data sets where T r + I n + F a < 1 . To achieve this goal, the F N s e t is recently introduced. This study employs the Interval-Valued Fermatean Neutrosophic Set ( I V F N s e t ) as its chosen framework to address instances of partial ignorance within the domains of truth, falsehood, or uncertainty. This selection stands out due to its unique approach to managing such complexities within multi-decision processes when compared to alternative methodologies. Furthermore, the proposed method reduces the propensity for information loss often encountered in other techniques. IVFNS excels at preserving intricate relationships between variables even when dealing with incomplete or vague information. In the present work, we introduce the I V F N s e t , which deals with partial ignorance in true, false, or uncertain regions independently for multi-decision processes. The I V F N s e t contains the interval-valued T r m e m b e r s h i p value, I n m e m b e r s h i p value, and F a m e m b e r s h i p for knowledge representation. The algebraic properties and set theory between the interval-valued F N s e t have also been presented with an illustrative example. [ABSTRACT FROM AUTHOR]

Secure dominance is a significant proportion of dominance which plays vital role in communication networks. In this article, we present and analyze an idea of the secured neutrosophic dominance and totally neutrosophic dominance number of neutrosophic graphs primarily based on strong arcs and the properties of both notions are studied. The terms 2- neutrosophic dominance number, 2- secured neutrosophic dominance variety, 2- totally neutrosophic dominance, and 2- secured neutrosophic dominance number also are defined. Some of their theoretical properties are investigated. [ABSTRACT FROM AUTHOR]

Simulation has become a modern-day tool that helps us study many systems that its results could not have been studied or predicted through the work of these systems over time. The simulation process depends on generating a series of random numbers that are subject to a uniform probability distribution on the field [0,1], and then converting these random numbers to random variables that follow the probability distribution in which the system to be simulated, there are several methods that can be used to carry out the conversion. In previous research, the inverse transformation method has been studied according to the Neutrosophic logic and we have reached Neutrosophic random variables, by using them we get a more accurate simulation of any system we want to simulate. It should be noted that the inverse transformation can be used if the cumulative distribution function has an inverse function, but if the system we want to simulate works according to a probability distribution, and the inverse function of the cumulative distribution function cannot be found, then we use other methods. In this research, we are examining a study that enables us to generate Neutrosophical random variables that follow probability distributions based on Neutrosophical random numbers that follow for the uniform distribution, using the rejection and acceptance method, which depends on the largest value taken by the probability density function of the distribution in which the system to be simulated operates on its definition. [ABSTRACT FROM AUTHOR]

Road traffic management has been a serious concern in the transportation sector for many years now. The explosion of the number of cars along with the inability of creating new highcapacity road infrastructures in big cities makes mitigating this danger a problem for the scientific research community. Traffic congestion contributes to increased pollution, economic loss, and a general deterioration in the quality of life. As a result, researchers are being asked to cope with the complexity of establishing effective and smooth traffic flow. However, as in traffic congestion control, real-world decision-making problems are always fraught with uncertainty and indeterminacy. The neutrosophic environment has been applied successfully to deal with these problems and recently, researchers tried to use various neutrosophic approaches to tackle the traffic congestion problem. This paper provides a brief overview of the most recently used neutrosophic techniques to handle traffic congestion and transportation problems in general. The aim of the investigation is to summarize the available neutrosophic traffic flow problems and their progress to enable future researchers to differentiate the major problems to be manipulated and identify conditions to be optimized. [ABSTRACT FROM AUTHOR]

Yager et. al. defined a q-rung orthopair fuzzy sets as a new general class of Pythagorean fuzzy set in which the sum of the qth power of the support for and support against is bonded by one. Tapan et. al. extended the concept of intuitionistic fuzzy sets as 3-rung orthopair fuzzy sets or Fermatean fuzzy sets (FFSs). Later C. Antony et. al. introduced the concept of Fermatean Neutrosophic Sets. In this work, we define Fermatean neutrosophic graphs and present some operations on Fermatean neutrosophic graphs. Further, we introduce the concepts of regular Fermatean neutrosophic graphs, strong Fermatean neutrosophic graphs, Cartesian, Composition, Lexicographic product of Fermatean neutrosophic graphs. Finally, we give the applications of Fermatean neutrosophic graphs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of balanced neutrosophic graphs based on density functions and investigate some of their properties. The necessary conditions for a neutrosophic graph to be a balanced neutrosophic graph are identified if graph G is a self-complementary, regular, complete, and strong neutrosophic graph. Some properties of complement neutrosophic graphs are presented here. [ABSTRACT FROM AUTHOR]

In this paper, we present a maple programming code that helps useres and scientific researchers to input single valued neutrosophic matrices, checks whether inputted matrix is single valued neutrosohic matrix, finds the complement of a single valued neutrosophic matrix, calculates score matrix, accuracy matrix and certainty matrix, finds the union and intersection of two single valued neutrosophic matrices, finds addition and product of two single valued neutrosophic matrices, also finds transpose of single valued neutrosophic matrix. This code is very important and useful in decision making problems that depend on single valued neutrosophic data. [ABSTRACT FROM AUTHOR]

The investigation of a person's symptoms can be evaluated through medical diagnosis to diagnose the diseases. To medical clinicians, a large amount of data is available for diagnosis, which comprises uncertainty, inconsistency, and indeterminacy. The field of medicine is one of the best areas of application for neutrosophic set theory. The main intention of this article is to deal with some of the applications of neutrosophic sets and their hybrid structures to solve medical diagnosis problems. [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]

In The traveling salesman problem (TSP) is an essential and the most popular conventional combinatorial optimization network problem in operations research, in which the TSP evaluates the shortest route or path in a network. In TSP, every node has been visited only once, excluding the starting node. In TSP, edge lengths are usually expressed to indicate journey time and expenses instead of distance from a location. The exact arc length can't be predicted because journey times and expenses vary depending on the amount of payload, climate, highway conditions, and so on. As a result, the Neutrosophic numbers introduce a new tool for dealing with unpredictability in TSP. The present article addresses TSP on a neutrosophic network where the edge weight is a neutrosophic number rather than a real number. For solving the Neutrosophic TSP, an algorithmic technique based on the genetic algorithm (GA) is proposed. We created a new mutation and crossover for our suggested GA. We used mathematical examples to show the usefulness of the algorithm that we suggested. The results of experiments suggest that the proposed GA can find the shortest path in a TSP within a neutrosophic framework. This provides valuable insights for decision-makers dealing with real-world situations characterized by imprecise and incomplete data. [ABSTRACT FROM AUTHOR]

The concepts of cubic spherical neutrosophic sets (CSNSs), introduced and investigated by Gomathi et al. [5], offer a geometric representation of collection of neutrosophic sets (NSs), enhancing their ability to capture uncertainty. The formulation characterizes information using points on a sphere with a defined center and radius, providing a more precise depiction of fuzziness inherent in uncertain data. The cubic spherical neutrosophic Archimedean triangular norms(ATN) and conorms (ATCN), expanding the model's capabilities to handle uncertainty. These algebraic operators enable the aggregation and combination of uncertain information, offering a more comprehensive approach to decision-making. The research further presents a method for solving multiple-criteria decision-making problems within the cubic spherical neutrosophic context, leveraging the newly integrated norms and conorms. The algorithm utilizes the cosine similarity measure of cubic spherical neutrosophic sets, exemplified through an application involving the selection of the most effective electric truck. This extended framework provides decision-makers with enhanced tools to navigate complex decision landscapes amidst uncertainty, facilitating more informed and robust choices across diverse domains. [ABSTRACT FROM AUTHOR]

In classical graph theory, the minimal spanning tree (MST) is a subgraph that lacks cycles and efficiently connects every vertex by utilizing edges with the minimum weights. The computation of a minimum spanning tree for a graph has been a pervasive problem over time. However, in practical scenarios, uncertainty often arises in the form of fuzzy edge weights, leading to the emergence of the Fuzzy Minimum Spanning Tree (FMST). This specialized approach is adept at managing the inherent uncertainty present in edge weights within a fuzzy graph, a situation commonly encountered in real-world applications. This study introduces the initial optimization approach for the Minimum Spanning Tree Problem within the context of interval-valued fermatean neutrosophic domain. The proposed solution involves the adaptation of the Dhouib-Matrix-MSTP (DM-MSTP) method, an innovative technique designed for optimal resolution. The DM-MSTP method operates by employing a column-row navigation strategy through the adjacency matrix. To the best of our knowledge, instances of this specific problem have not been addressed previously. To address this gap, a case study is generated, providing a comprehensive application of the novel DM-MSTP method with detailed insights into its functionality and efficacy. [ABSTRACT FROM AUTHOR]

Parameter reduction can be treated as an effective tool in many fields, including pattern recognition. Many reduction techniques have been reported so far for soft sets, fuzzy soft sets and bipolar fuzzy soft sets to solve decision-making problems. However, there is almost no attention to the parameter reduction of neutrosophic soft sets. In this present paper we focus our discussion on the parameter reduction of neutrosophic soft sets as an extension of parameter reduction of soft sets and fuzzy soft sets. To do that, using the concept of indiscernibility relation, we first define the terms 'dispensable set' and 'indispensible set'. We utilize these definitions to define the terms 'decision partition', 'parameter reduction' and 'degree of importance of a parameter' with a suitable example. Next we present an algorithm based on the concept of degree of importance and parameter reduction of a neutrosophic soft set. An illustrative example is employed to show the feasibility and validity of our proposed algorithm based on parameter reduction of neutrosophic soft sets in real life decision making problem. [ABSTRACT FROM AUTHOR]

Neutrosophic cubic fuzzy sets (NCFSs) involve interval valued and single valued neutrosophic sets, and are used to describe uncertainty or fuzziness in a more efficient way. Aggregation of neutrosopic cubic fuzzy information is crucial and necessary in a decision making theory. In order to get a better solution to decision making problems under neutrosophic cubic fuzzy environment, this paper introduces an aggregating operator to neutrosophic cubic fuzzy sets with the help of Bonferroni mean and geometric mean, and proposes neutrosophic cubic fuzzy geometric Bonferroni mean operator (NCFGBMu;v) with its properties. Then, an efficient decision making technique is introduced based on weighted operator WNCFGBMwu;v. An application of the established method is also examined for a real life problem. [ABSTRACT FROM AUTHOR]

A neutrosophic set is a part of neutrosophy that studies the origin, nature and scope of neutralities as well as their interactions with different ideational spectra. In this present paper first we have introduced the concept of a neutrosophic soft set having incomplete data with suitable examples. Then we have tried to explain the consistent and inconsistent association between the parameters. We have introduced few new definitions, namely- consistent association number between the parameters, consistent association degree, inconsistent association number between the parameters and inconsistent association degree to measure these associations. Lastly we have presented a data filling algorithm. An illustrative example is employed to show the feasibility and validity of our algorithm in practical situation. [ABSTRACT FROM AUTHOR]

In this research article we actually deals with the conception of pentagonal Neutrosophic number from a different frame of reference. Recently, neutrosophic set theory and its extensive properties have given different dimensions for researchers. This paper focuses on pentagonal neutrosophic numbers and its distinct properties. At the same time, we defined the disjunctive cases of this number whenever the truthiness, falsity and hesitation portion are dependent and independent to each other. Some basic properties of pentagonal neutrosophic numbers with its logical score and accuracy function is introduced in this paper with its application in real life operation research problem which is more reliable than the other methods. [ABSTRACT FROM AUTHOR]

Bipolar neutrosophic matrices (BNM) are obtained by bipolar neutrosophic sets. Each bipolar neutrosophic number represents an element of the matrix. The matrices are representable multi-dimensional arrays (3D arrays). The arrays have nested list data type. Some operations, especially the composition is a challenging algorithm in terms of coding because there are so many nested lists to manipulate. This paper presents a Python tool for bipolar neutrosophic matrices. The advantage of this work, is that the proposed Python tool can be used also for fuzzy matrices, bipolar fuzzy matrices, intuitionistic fuzzy matrices, bipolar intuitionistic fuzzy matrices and single valued neutrosophic matrices. [ABSTRACT FROM AUTHOR]

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed by F. Smarandache to represent imprecise, incomplete and inconsistent information existing in the real world. A neutrosophic set is characterized by a truth-membership function, an indeterminacymembership function, and a falsity-membership function. An interval neutrosophic set is an instance of a neutrosophic set, which can be used in real scientific and engineering applications. In this paper we have defined some new operators on interval valued neutrosophic sets and studied their properties. In addition, we give numerical examples to illustrate the defined operations. [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]

Graph theory is a developing field which has many advancements and developments in real-life applications. Although graph theory has rapid growth in modeling real-life issues, some vague details in real-life problems are hard to picture using the usual graph. Fuzzy graph theory is known for its applications in modeling the human thinking, which has the same structure as graph theory. The concept of fuzzy graphs extended to Pythagorean fuzzy sets depends on real-time situations. The purpose of interval-valued Pythagorean neutrosophic sets through which the values of the degree (membership, non-membership and neutral) can be taken from the intervals instead of the numbers so that it provides more adequate information about the uncertainty than traditional sets. This motivates us to introduce interval-valued Pythagorean neutrosophic sets in applications. The proposed investigation also leads to study the interval-valued Pythagorean neutrosophic graphs (IVPNGs) and their arithmetic operations. In addition, the concept of regular, strong, product, support strong, effective balanced IVPNGs are introduced for aggregating the IVPNGs information and analysed with suitable examples. Further, a methodology for successful curriculum design is examined to illuminate the adequacy and feasibility of the developed IVPNG. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article enriches the idea of neutrosophic soft ideal (NSI). The notion of neutrosophic soft prime ideal (NSPI) is also introduced here. The characteristics of both NSI and NSPI are investigated. Their relations are drawn with the concept of ideal and prime ideal in crisp sense. Any neutrosophic soft set (Nss) can be made into NSI or NSPI using the respective cut set under a situation. The homomorphic characters of ideal and prime ideal in this new class are also drawn critically. [ABSTRACT FROM AUTHOR]

In recent time graphical analytics of uncertainty and indeterminacy has become major concern for data analytics researchers. In this direction, the mathematical algebra of neutrosophic graph is extended to interval-valued neutrosophic graph. However, building the interval-valued neutrosophic graphs, its spectrum and energy computation is addressed as another issues by research community of neutrosophic environment. To resolve this issue the current paper proposed some related mathematical notations to compute the spectrum and energy of interval-valued neutrosophic graph using the MATAB. [ABSTRACT FROM AUTHOR]

In the last decade, characterizing the energy in MANET based on its acceptation, rejection and uncertain part is addressed as one of the major issues by the researchers. An efficient energy routing protocol for MANET is another issue. To resolve these issues current paper focuses on utilizing the properties of neutrosophic technique. The essential idea of the protocol is to choose an energy efficient route with respect to neutrosophic technique. In this neutrosophic set, we have three components such as (T, I, F). Each parameter such as energy and distance is taken from these neutrosophic sets to determine the efficient energy route in MANET. After taking a brief survey about energy efficient routing for MANET using various methods, we are trying to implement the neutrosophic set technique to find the efficient energy route for MANET which provides the better energy route in uncertain situations. The comparative analysis between vague set MANET and neutrosophic MANET for the values of energy functions and distance functions is done by using Matlab and the result is discussed graphically. [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]

The discovery of soft sets is accredited to Molodtsov. This theory can cope with difficult circumstances with a lot of ambiguity, like those where deciding is hard. The bipolar soft set (BSS) and neutrosophic soft set (NSS) are algebraic models that can be viewed as soft set expansions. The BSS theory states that we weigh the pros and cons when deciding and NSS theory can handle belief system ambiguity, contradiction, and lack of knowledge due to its truth and falsity membership values. The concept of BSS and NSS are explained in comprehensive detail in this article. This article examined the weighted bipolar soft set (WBSS) and the weighted neutrosophic soft set (WNSS), as well as how to make accurate decisions under uncertain or inadequate information. A detailed comparison of information extraction approaches using weighted bipolar and neutrosophic soft sets may be lacking in the literature. These strategies may have been studied separately, but there may be little research comparing their performance under different settings and with diverse data. Filling this gap with a thorough and rigorous comparison study would help comprehend these techniques' practical benefits and drawbacks. [ABSTRACT FROM AUTHOR]

Neutrosophic set is a generalization of classical set, fuzzy set, and intuitionistic fuzzy set by employing a degree of truth (T), a degree of indeterminacy (I), and a degree of falsehood (F) associated with an element of the dataset. One of the most essential problems is studying set-theoretic operators in order to be applied to practical applications. Developing Matlab toolboxes for computing the operational matrices in neutrosophic environments is essential to gain more widely-used of neutrosophic algorithms. In this paper, we propose some computing procedures in Matlab for neutrosophic operational matrices, especially i) computing the single-valued neutrosophic matrix; ii) determining complement of a single-valued neutrosophic matrix; iii) computing max-min-min and min-maxmax of two single-valued neutrosophic matrices; v) computing power of a single-valued neutrosophic matrix; vi) computing additional operation and subtraction of two single-valued neutrosophic matrices; and ix) computing transpose of a singlevalued neutrosophic matrix. Numerical examples are given to illustrate their applicability. [ABSTRACT FROM AUTHOR]

The most well-known subject in graph theory is the shortest path problem (SPP), which has real-world applications in several different fields of study, including transportation, emergency services, network communications, fire station services, etc. The arc weights of the applicable SP problems are typically represented by fuzzy numbers in real-world applications. In this paper, we discussed the process of finding the shortest distance in a connected graph network in which the arc weights are multi-valued neutrosophic numbers (MNNs). Moreover, here we compare our method with some of the existing results and illustrate one implementation of our method with the help of one numerical example. [ABSTRACT FROM AUTHOR]

The shortest path (SP) problem (SPP) has several applications in graph theory. It can be used to calculate the distance between the provided initial and final vertex in a network. In this paper, we employed the Fermatean neutrosophic number as the appropriate edge weight of the network to estimate the SP connecting the start and end vertex. This technique is highly useful in establishing the shortest path for the decision-maker under uncertainty. We also investigated its effectiveness in comparison to several existing methods. Finally, a few numerical tests were performed to demonstrate the validity and stability of this new technique, as well as to compare different types of shortest paths with different networks. [ABSTRACT FROM AUTHOR]

Multicriteria group decision-making scenarios with a large number of criteria values may be challenging for experts to control. This is a result of the specialists' need to consider an excessive amount of data. They find it difficult to make the optimal decision since the possibilities overwhelm them. We propose a novel multicriteria group decisionmaking method that methodically eliminates the initial set of criterion values in order to address this issue. One of the most promising emerging technologies currently in development is an additive manufacturing (AM), which includes 3D printing. It has been hypothesized that 3D printing technology could eventually replace the conventional production machinery that is commonly used in the industrial sector. Making conclusions through accurate figures is difficult for decision-makers due to the complexity and ambiguity of reality. Neutrosophic ensembles are used to tackle uncertainty and indeterminacy in a practical environment. By concentrating on ranking the smaller set of criterion values, the proposed method enables the experts to carry out the group decision-making process. As a result, a relaxed decision-making environment is created, allowing the experts to handle a reasonable amount of information while still making decisions. To demonstrate the decision process of a 3D printer, we combine a single valued Neutrosophic with hybrid score and accuracy function, the single valued Neutrosophic number ranking approach, and the single valued Neutrosophic score and accuracy function. To determine the best attributes, the score function was used to rank the total values of each possibility. Concrete examples have been given to support the suggested solution to the multi-attribute decision-making problem (MADM). [ABSTRACT FROM AUTHOR]

The concepts of neighbourly irregular neutrosophic graphs, neighbourly totally irregular neutrosophic graphs, highly irregular neutrosophic graphs and highly totally irregular neutrosophic graphs are introduced. A criteria for neighbourly irregular and highly irregular neutrosophic graphs to be equivalent, is discussed. [ABSTRACT FROM AUTHOR]

The interval valued neutrosophic graphs are generalizations of the fuzzy graphs, interval fuzzy graphs, interval valued intuitionstic fuzzy graphs, and single valued neutrosophic graphs. Previously, several results have been proved on the isolated graphs and the complete graphs. In this paper, a necessary and sufficient condition for an interval valued neutrosophic graph to be an isolated interval valued neutrosophic graph is proved. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a subclass of interval valued neutrosophic graphs called strong interval valued neutrosophic graphs, which were introduced by Broumi et al. [41]. The operations of Cartesian product, composition, union and join of two strong interval valued neutrosophic graphs are defined. Some propositions involving strong interval valued neutrosophic graphs are stated and proved. [ABSTRACT FROM AUTHOR]

The notion of interval valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued fuzzy sets, interval valued intuitionstic fuzzy sets and single valued neutrosophic sets. We apply for the first time to graph theory the concept of interval valued neutrosophic sets, an instance of neutrosophic sets. We introduce certain types of interval valued neutrosophc graphs (IVNG) and investigate some of their properties with proofs and examples. [ABSTRACT FROM AUTHOR]

Many results have been obtained on isolated graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph. [ABSTRACT FROM AUTHOR]

In this paper a new concept is called n-valued interval neutrosophic sets is given. The basic operations are introduced on n-valued interval neutrosophic sets such as; union, intersection, addition, multiplication, scalar multiplication, scalar division, truthfavorite and false-favorite. Then, some distances between n-valued interval neutrosophic sets (NVINS) are proposed. Also, we propose an efficient approach for group multi-criteria decision making based on n-valued interval neutrosophic sets. An application of n-valued interval neutrosophic sets in medical diagnosis problem is given. [ABSTRACT FROM AUTHOR]

In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya's distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on the comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better and more robust. An illustrative example of the pattern recognition shows that the proposed method is simple and effective. [ABSTRACT FROM AUTHOR]

In this paper, we extend the lower and upper soft interval valued intuitionstic fuzzy rough approximations of IVIFS -relations proposed by Anjan et al. to the case of interval valued neutrosophic soft set relation(IVNSS-relation for short) [ABSTRACT FROM AUTHOR]

In this paper we proposed a new distance and several similarity measures between interval neutrosophic sets. [ABSTRACT FROM AUTHOR]

The interval neutrosophic uncertain linguistic variables can easily express the indeterminate and inconsistent information in real world, and TOPSIS is a very effective decision making method more and more extensive applications. In this paper, we will extend the TOPSIS method to deal with the interval neutrosophic uncertain linguistic information, and propose an extended TOPSIS method to solve the multiple attribute decision making problems in which the attribute value takes the form of the interval neutrosophic uncertain linguistic variables and attribute weight is unknown. Firstly, the operational rules and properties for the interval neutrosophic variables are introduced. Then the distance between two interval neutrosophic uncertain linguistic variables is proposed and the attribute weight is calculated by the maximizing deviation method, and the closeness coefficients to the ideal solution for each alternatives. Finally, an illustrative example is given to illustrate the decision making steps and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets(SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets. [ABSTRACT FROM AUTHOR]

In this paper, the cosine similarity measure of neutrosophic refined (multi-) sets is proposed and its properties are studied. The concept of this cosine similarity measure of neutrosophic refined sets is the extension of improved cosine similarity measure of single valued neutrosophic. Finally, using this cosine similarity measure of neutrosophic refined set, the application of medical diagnosis is presented. [ABSTRACT FROM AUTHOR]

In this study, we introduce the concept of neutrosophic soft multi-set theory and study their properties and operations. Then, we give a decision making methods for neutrosophic soft multi-set theory. Finally, an application of this method in decision making problems is presented. [ABSTRACT FROM AUTHOR]

In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya's distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on inthe comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better and more robust. An illustrative example of the pattern recognition shows that the proposed method is simple and effective. [ABSTRACT FROM AUTHOR]