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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]

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]

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]

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]

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]

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]

Municipal solid waste management (MSWM) has emerged as a major issue in India due to the massive amounts of waste generated on a daily basis. Governments are focusing on establishing a proper waste management system, including a timeline for the installation of waste processing and disposal facilities to reduce waste. For this problem, waste to energy (WtE) technologies have been identified because of their ability to convert waste into green energy while minimizing associated issues. This research investigates the different kinds of WtE treatments based on various factors, namely eco-friendly, budget friendly, technical, and social aspects. The findings of this study revealed which WtE treatments are best suited for waste management systems that convert green energy. In this paper, we propose the best WtE treatment for India using the interval-valued pythagorean neutrosophic fuzzy set (PNFS). We employ the WASPAS-CRITIC method in the interval-valued pythagorean neutrosophic fuzzy environment for this WtE treatment problem. Finally, a numerical example and a comparison are provided to illustrate the reliability and efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

Uncertain and ambiguous data is usually presented as a data point. When dealing with uncertain data, it is challenging to deal with incompleteness, imprecision, and incertitude; therefore, various mathematical models were developed to resolve issues concerning uncertainty points. To overcome this difficulty, a mathematical model with redefined control points characterised by three important components of the neutrosophic set was produced. The neutrosophic set can then be translated by creating models based on the neutrosophic theory and its relationships to produce control points. Hence, this paper represents a curve generated by combining neutrosophic control points with the B'ezier basic functions using their relation as a Neutrosophic B'ezier Curve. With an illustration example, we show how to visualise neutrosophic data sets into Neutrosophic B'ezier Curve and their relationship. [ABSTRACT FROM AUTHOR]

The characterization of interval valued (IV) secondary k- range symmetric (RS) Neutrosophic fuzzy matrices have been examined in this study with an example. It is discussed how IV s-k RS, s- RS, IV k- RS, and IV RS matrices relate to one another. We establish the necessary and sufficient criteria for IV s-k RS Neutrosophic fuzzy matrices. The existence of several generalized inverses of a matrix in IV Neutrosophic fuzzy matrices. It is also established what are the equivalent criteria for various g-inverses of an IV s - κ RS fuzzy matrix to be an IV s - κ RS. The generalized inverses of an IV s - κ RS P corresponding to the sets P{1, 2}, P{1, 2, 3} and P{1, 2, 4} are characterized. [ABSTRACT FROM AUTHOR]

Neutrosophic sets play a crucial role in handling uncertainty, ambiguity, and indeterminacy in numerous theories. They are a kind of extension of the two types of fuzzy sets and intuitionistic fuzzy sets. In the context of modeling drug diffusion within human connective tissues, a differential equation is employed within the neutrosophic framework, utilizing Hukuhara differentiability. We establish the initial conditions and parameters in the form of Type 2 triangular single-valued neutrosophic numbers. This study explores the stability and existence of equilibrium points, providing precise solutions. To conduct numerical simulations across various values of the (α, β, γ)-cut of the triangular neutrosophic number, we utilize MATLAB 2018a. [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]

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 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]

We develop the concept of range symmetric Neutrosophic Fuzzy Matrix and Kernel symmetric Neutrosophic Fuzzy Matrix analogous to that of an EP -matrix in the complex field. First we present equivalent characterizations of a range symmetric matrix and then derive equivalent conditions for a Neutrosophic Fuzzy Matrix to be kernel symmetric matrix and study the relation between range symmetric and kernel symmetric Neutrosophic Fuzzy Matrices. The idea of Kernel and k-Kernel Symmetric (k-KS) Neutrosophic Fuzzy Matrices (NFM) are introduced with an example. We present some basic results of kernel symmetric matrices. We show that k-symmetric implies k-Kernel symmetric but the converse need not be true. The equivalent relations between kernel symmetric, k-kernel symmetric and Moore-Penrose inverse of NFM are explained with numerical results. [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]

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]

In this paper we have successfully constructed the literal neutrosophic Kumaraswamy probability distribution. We mean by literal neutrosophic probability distribution that parameters of the distribution and the values that the random variable describing the distribution all take literal neutrosophic numbers of the form θ = q + bl; I² = I which differs from interval-valued neutrosophic probability distributions in which parameters of theses distributions take the form θN 8712; [L, U]. We have derived the neutrosophic form of the probability density function, cumulative distribution function, statistical properties and maximum likelihood estimations of the parameters. Finally, a simulation study is performed to show the efficiency of the estimators provided by the neutrosophic MLE method. [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]

Currently most signalized intersections in almost all developing countries use fixed time traffic controllers or pre-timed traffic lights. But as a real life situation, in addition to uncertainty and impreciseness there is also indeterminacy in traffic signal control constraints due to various factors like unawareness of the problem, inaccurate and imperfect data and poor forecasting in addition to uncertainty in the constraints. To overcome these interval valued neutrosophic soft set traffic signal control model at four way isolated signalized intersections has been developed. The main aim of this research is to validate the IVNSS traffic signal control model and compare it with fixed time trafic signal control model using MATLAB simulation tool. Vehicle delay at the junction is used as a measure of efiectiveness. The simulation is conducted for seven consecutive days from Monday up to Sunday for eight hours to reflect the difierent trafic flow conditions. The simulated delay model results are analysed under 5 different scenarios. And results showed that in case of heavy trafic conditions vehicle delay under IVNSS trafic signal control model is minimized by 36 percent and under light trafic conditions the average vehicle delay is minimized by 73 percent when compared to fixed time trafic signal control model. [ABSTRACT FROM AUTHOR]

Aggregation operators can be used to combine and synthesise a finite number of numerical values into a single numerical value. Many areas, including decision-making, expert systems, risk analysis, and image processing, rely heavily on aggregating functions. In real-world situations, the neutrosophic set can manage the uncertainties associated with information from any decision-making challenge, whereas the fuzzy set and intuitionistic set cannot. The term "bipolarity" refers to the propensity of the human mind to weigh pros and drawbacks when thinking through decisions. Triangular norms are aggregation operators in a variety of fields, including fuzzy set theory, probability and statistics, and decision sciences. Thus, the individual assessments in this paper's study of and approach to multi-criteria decision-making (MCDM) problems that use bipolar neutrosophic numbers as the individual evaluations. Frank operational laws of bipolar neutrosophic numbers, bipolar neutrosophic Frank weighted geometric aggregation (BNFWGA) and the bipolar neutrosophic frank ordered weighted geometric aggregation (BNFOWGA) operators have been developed with its desirable properties. Additionally, the suggested aggregation operators have been used in the selection of bridges. The outcomes demonstrate the applicability and validity of the suggested approach. Comparative analysis has been performed using the current approach. [ABSTRACT FROM AUTHOR]

The quadripartitioned neutrosophic set is the partition of indeterminacy function of the neutrosophic set into contradiction part and ignorance part. In this work, the concept of quadripartitioned neutrosophic graph structures and its properties are invented. The strong, tree, ϕ - permutation and ϕ - complement of quadripartitioned neutrosophic graph structure are investigated. The operations like Cartesian Product, cross product, lexicographic product, composition in graph structures and join operations are established. [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]

This study included concepts for (ϖ, ε, ς )-single valued neutrosophic hyperring ((ϖ, ε, ς )-SVNHR) and (ϖ, ε, ς )-single valued neutrosophic hyperideal ((ϖ, ε, ς )-SVNHI). (ϖ, ε, ς )-single valued neutrosophic hyperrings ((ϖ, ε, ς )-SVNHRs) and (ϖ, ε, ς)-single valued hyperideals ((ϖ, ε, ς )-SVNHIs) are examined and validated in terms of algebraic features and of structural characteristics. [ABSTRACT FROM AUTHOR]

The notion of neutrosophic algebra, ideal of neutrosophic algebra, kernel and neutrosophic quotient algebra have been proposed in this paper. We characterize some properties of neutrosophic algebra and proved that every quotient neutrosophic algebra is quotient algebra. Also we proved that every neutrosophic algebra is algebra and direct product of neutrosophic algebras over a neutrosophic field is algebra. [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]

The aim of this paper is to develop many characterizations of Pentapartitioned Neutrosophic Pythagorean (PNP) strongly irresolvable spaces and its properties is also studied. Several characterizations of Pentapartitioned Neutrosophic Pythagorean strongly irresolvable spaces are investigated in this study. Also examined are the conditions under which Pentapartitioned Neutrosophic Pythagorean strongly irresolvable spaces become Pentapartitioned Neutrosophic Pythagorean first category spaces, Pentapartitioned Neutrosophic Pythagorean Baire spaces, and Pentapartitioned Baire spaces. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of reliable nodes in neutrosophic soft graphs by evaluating path-based parameters. A reliable node is defined as one which is least susceptible to changes that are quantized by the indeterminacy and falsity values in a neutrosophic tuple. A new path measure called farness and three novel reliability measures which make use of the same are presented. Farness is defined in terms of a novel score function. The first, proximity reliability of a node, computes the farness of a node to its neighbours. The second, intermediate reliability of a node, computes the fraction of paths of minimal farness that pass through it. The third, crisis reliability of a node, is a hybrid of the two previously defined. It considers the farness of a node to its neighbours taking into account the farness of the neighbours to other nodes in the graph. [ABSTRACT FROM AUTHOR]

In this article some Dombi operations on Quadripartitioned single valued neutrosophic (QSVN) set are studied. Later on some QSVN weighted Dombi operators i.e. QSVNWDA and QSVNWDG operators are introduced and their properties are studied. Finally a vaccine distribution technique is solved with the help of QSVNWDA operator and QSVNWDG operator. [ABSTRACT FROM AUTHOR]

Let G = (U, V) be a Single valued Neutrosophic graph. A subset S ∈ U(G) is a said to be score equitable set if the score value of any two nodes in S differ by at most one. That is, |s(u)- s(v)| ≤ 1, u, v ∈ S. If e is an edge with end vertices u and v and score of u is greater than or equal to score of v then we say u strongly dominates v. If every vertex of V - S is strongly influenced by some vertex of S then S is called strong score set of G. The minimum cardinality of a strong dominating set is called the strong score number of G. The equitable integrity of Single valued Neutrosophic graph G which is defined as EI(G) = min{|S| + m(G - S): S is a score equitable set in G}, where m(G - S) denotes the order of the largest component in G - S. The strong integrity of Single valued Neutrosophic graph G which is defined as SI(G) = min{|S| + m(G - S): S is a strong score set in G}. In this paper, we study the concepts of equitable integrity and strong equitable integrity in different classes of regular Neutrosophic graphs and discussed the upper and lower bounds. [ABSTRACT FROM AUTHOR]

In 1998, Smarandache introduced the new theory - Neutrosophic sets. In order to achieve the best results in a current situation, policy makers must contend with uncertainty and unpredictability. The neutrosophic definition aids in the investigation of ambiguous or indeterminate values. Here, we have the amalgamated the theory of Single Valued Neutrosophic Vertex Coloring and r-dynamic coloring to introduce a new thought Single Valued Neutrosophic R-dynamic Vertex Coloring (SVNRVC) and have shown example. Further we have determined the Single Valued Neutrosophic R-dynamic chromatic number χR(G) for some graphs. [ABSTRACT FROM AUTHOR]

In this article the notion of two quadripartitioned single valued weighted dombi prioritized operators, namely, quadripartitioned single valued weighted dombi prioritized average (QSVNWDPA) operator and quadripartitioned single valued weighted dombi prioritized geometric (QSVNWDPG) operator have been developed which are based on quadripartitioned single valued neutrosophic (QSVN) sets. Further some important properties of these two operators are studied. Finally a multi-attribute decision making (MADM) problem has been solved using QSVNWDPA operator and QSVNWDPG operator. [ABSTRACT FROM AUTHOR]

The similarity measure is used to tackle many issues that include indistinct as well as blurred information excluding is not in a position to deal with the general fuzziness along with obscurity of the problems that have various information. The main purpose of this research is to propose a multipolar interval-valued neutrosophic soft set (mPIVNSS) with operations and basic properties. We also develop Hamming distance and Euclidean distance by using mPIVNSS and numerical examples and use the developed distances to introduce similarity measures. By using the developed similarity measures a decision-making approach is presented for mPIVNSS. Finally, we used the developed decision-making approach for medical diagnosis. [ABSTRACT FROM AUTHOR]

One of the highest causes of death in many countries in this modern era is cardiovascular diseases. There are a few symptoms that linked significantly to the cardiovascular diseases. The symptoms and diseases relationship can be represented by neutrosophic set values. In general, neutrosophic set gives remarkable contribution in denoising, clustering, segmentation, and classification in handling data of many real applications including in medical field. This study aims to analyse the cardiovascular disease risks by a new distance-based similarity measure motivated from intuitionistic fuzzy set theory. The proof for all the properties is presented clearly. Then, a case study is conducted by using the data on the severity level of the six symptoms found in two different patients. The neutrosophic data are analysed to determine the patients' possibility of having any one or combination of the three types of cardiovascular diseases. A comparative study involving three common distance measures is conducted. The results show that the similarity indexes for all measures of both patients are less than 0.5. This situation can further conclude as both patients are possibly not suffering from cardiovascular diseases. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of Pentapartitioned Neutrosophic Pythagorean resolvable, Pentapartitioned Neutrosophic Pythagorean irresolvable, Pentapartitioned Neutrosophic Pythagorean open hereditarily irresolvable and maximally Pentapartitioned Neutrosophic Pythagorean irresolvable spaces are introduced. Also we investigated several properties of the Pentapartitioned Neutrosophic Pythagorean open hereditarily irresolvable spaces besides giving characterization of these spaces by means of somewhat Pentapartitioned Neutrosophic Pythagorean continuous functions and somewhat Pentapartitioned Neutrosophic Pythagorean open functions [ABSTRACT FROM AUTHOR]

The concept of Neutrosophic Pythagorean set [NPS] with dependent Neutrosophic Pythagorean components was introduced and discussed the relationship between dependent neutrosophic and neutrosophic pythagorean components. The correlation coefficient is a statistical measure which contributes in deciding the degree to which changes in one variable predict changes in another. In this article, we analyze the characteristics of neutrosophic pythagorean sets with improved correlation coefficients. We've also used the same approach in multiple attribute decisionmaking methodologies including one with a neutrosophic pythagorean environment. Finally, we implemented for above technique to the problem of multiple attribute group decision making. [ABSTRACT FROM AUTHOR]

The correlation coefficient among the two parameters plays a significant part in statistics. Further, the exactness in the assessment of correlation depends upon information from the set of discourse. The data collected for various statistical studies is full of ambiguities. In this paper, we discuss some basic concepts which are helpful to build the structure of present research such as soft set, hypersoft set, and neutrosophic hypersoft set (NHSS). The neutrosophic hypersoft set is an extension of the neutrosophic soft set. In it, we establish the idea of correlation and weighted correlation coefficients with some desirable properties under NHSS. We also, propose a new decision-making technique and construct an algorithm based on developed correlation measures. Furthermore, To ensure the applicability of the proposed methods an illustrative example is given. [ABSTRACT FROM AUTHOR]

A single-valued neutrosophic set is one of the advanced fuzzy sets that is capable of handling complex real-world information satisfactorily. A development of single-valued neutrosophic set and fuzzy bipolar set, called a bipolar neutrosophic set, was introduced. Distance measures between fuzzy sets and advanced fuzzy sets are important tools in diagnostics and prediction problems. Sometimes they are defined without considering the condition of the inclusion relation on sets. In decision-making applications, this condition should be required (here it is called the inference of the measure). Moreover, in many cases, a distance measure capable of discriminating between two nearly identical objects is considered an effective measure. Motivated by these observations, in this paper, a new distance measure is proposed in a bipolar neutrosophic environment. Furthermore, an entropy measure is also developed by the similarity between two sets of mutual negation. Finally, an application to medical diagnosis is presented to illustrate the effective applicability of the proposed distance measure, where entropy values are used to characterize noises of different attributes. [ABSTRACT FROM AUTHOR]

In this paper, some types of edge irregular single valued neutrosophic graphs such as neighbourly edge totally irregular single valued neutrosophic graphs, strongly edge irregular single valued neutrosophic graphs and strongly edge totally irregular single valued neutrosophic graphs are introduced. A comparative study between neighbourly edge irregular single valued neutrosophic graphs and neighbourly edge totally ir- regular single valued neutrosophic graphs is done. Likewise some properties of them are studied. Finally, we have given some interesting results about edge irregular single valued neutrosophic graphs that are very useful in computer science and networks. [ABSTRACT FROM AUTHOR]

As far world history is concerned, human being faced many problems like world war, terrorist attack, bomb blasters, natural disasters and so on. But all these problems are visible and were able to come across in few months or years. Nowadays situation is entirely different from the past world history, because all the worlds are fighting with an invisible enemy called Novel Corono virus disease (Covid-19). If we compare with other diseases like Swine flu, Ebola virus this disease is very infectious and the death rate is also severe all around the world. The covid-19 pandemic has affected everyone both physically, mentally and changed our life style. Almost all the countries are suffering from this disease and the countries are struggling to control from this epidemic. Researchers in all the disciplines are exploring ways to control this disease and trying to find a vaccine. So this is a correct situation to mathematically analyze the disease covid-19 like symptoms, spreading way and precaution method using Fuzzy cognitive maps and Neutrosophic cognitive maps. Both the methods work on expert’s opinion. Since medical field involves uncertainty and indeterminacy, we have chosen fuzzy set and neutrosophic sets for our study. [ABSTRACT FROM AUTHOR]

In this paper, the notion of the interval valued complex neutrosophic soft set (IV-CNSS) is defined as a combination of interval valued complex neutrosophic set and soft set. Then, we introduce the IV-CNSS's operations such as union, intersection and complement. To explore the study further, we present some basic operational rules, and investigate their properties. A new algorithm is developed by transforming the interval complex neutrosophic soft values from complex space to the real space using a practical formula which gives a decision-making with a simple computational process without the need to carry out directed operations by complex numbers. This algorithm is then applied to evaluate two kinds of a certain product from a manufacturer and choose the most suitable one. IV-CNSS provides an interval-based membership structure to handle the uncertain data. This feature allows decision makers to record their hesitancy in assigning membership values which in turn best catch the obscurity and the complexity of such data. [ABSTRACT FROM AUTHOR]