International Journal of Neutrosophic Science

Whether for human consumption, agricultural production, or industrial processes, groundwater, and rivers, in particular, are crucial. The river is a major water source; therefore, we must do all we can to keep it clean. Inconsistencies in data, algorithms and expert judgments have contributed to the growing recognition of ambiguity analysis' significance. However, it is not common practice to include vulnerability assessment in MCA based Interval-Valued Neutrosophic Sets (IVNSs). To better understand what causes MCA uncertainty, this research examines the factors that contribute to it. Probabilistic techniques, indicator-based methods, and neutrosophic logic are examined as examples of broad approaches to analysis methods in MCA. The practicality, financial and ecological consequences, unexpected social and environmental implications, possible scale of change, and confirmation of the impact of plastic reduction strategies were investigated using an MCA technique.

The goal of this work the critical criteria that affect social sports competition organization's arrangement. Then determine the relations between criteria with others and alternatives. So, the evaluation of the process of social sports competition contains many conflict criteria. The multi-criteria decision-making (MCDM) process is an effective tool for dealing with conflict and complex criteria. This work employs a new integrated model for dealing with the problem in an analytical hierarchal process (AHP) and Višekriterijumsko Kompromisno Rangiranje (VIKOR) methods under single-valued neutrosophic sets (SVNSs). SVNSs are the best tool for overcoming uncertainty and incomplete information. The AHP method is used for computing the weights of criteria then VIKOR is used for rank alternatives. The twelve criteria and five alternatives are used in this problem. An illustrative example is provided to present a robust hybrid model. This paper can help organizations and countries for arrangement and organize social sports completion with a scoring system design.

A well known and referenced global result is the nilpotent characterisation of the finite p-groups. This undoubtedly transends into neutrosophy. Hence, this fact of the neutrosophic nilpotent p-groups is worth critical studying and comprehensive analysis. The nilpotent characterisation depicts that there exists a derived series (Lower Central) which must terminate at {ϵ} ( an identity ) , after a finite number of steps. Now, Suppose that G(I) is a neutrosophic p-group of class at least m ≥ 3. We show in this paper that Lm−1(G(I)) is abelian and hence G(I) possesses a characteristic abelian neutrosophic subgroup which is not supposed to be contained in Z(G(I)). Furthermore, If L3(G(I)) = 1 such that pm is the highest order of an element of G(I)/L2(G(I)) (where G(I) is any neutrosophic p-group) then no element of L2(G(I)) has an order higher than pm.

This study aims to propose a new entropy weight on the distance measure of single value neutrosophic set (SVNS) to analyse medical diagnosis patient’s risk. Four distance measures will be integrated with three entropy weight concepts and applied to medical diagnosis. A new entropy weight measure integrated with the four distance measures are calculated using the medical data of one patient with five symptoms and five diseases. The calculated new entropy and its associated distance measures give consistent finding with the existing entropy weight measures. However, all the values are even smaller showing that the relation between patient A and disease are stronger. This evaluation and diagnosis approach is applicable to a wide variety of other resources and medical problems.

The main idea of this paper is to introduce neutrosophic binary αgs-neighborhood points and neutrosophic binary αgs interior and closure operators. Furthermore, some of its properties are contemplated.

Interval-valued neutrosophic sets (IVNSs) are a notion that was initially developed by Wang et al.19 The idea of IVNSs to deductive systems (DSs) in Hilbert algebras is presented in this study. It is shown how intervalvalued neutrosophic deductive systems (IVNDSs) relate to their level cuts. In addition, certain related features are examined as well as the homomorphic inverse image of IVNDSs in Hilbert algebras.

Social responsibility is the most important thing to consider while working on a project. When deciding on a project or taking part in a bid, it is crucial to understand the nature and potential consequences of the risks involved. Attempting to implement projects with cutting-edge technologies appears to be necessary, necessitating up-to-date and continuous planning to implement the relevant matters in light of the ever-increasing growth of urban communities, the need to carry out tasks, and the rising standard of living. Due to the strong demand, these strategies try to improve quality while decreasing prices. In the beginning, Smarandache suggests using neutrosophic sets. These sets are an improvement above traditional fuzzy set theory in reflecting the uncertainty and fuzziness of real-world issues. Three decision-making states are considered: uncertainty, truthiness, and falseness. The fuzzy set degree in Zadeh's classic theory is merely the membership function. On the other hand, three membership functions are considered in a neutrosophic setting. An indeterminacy degree is considered, which is not the case with intuitionistic fuzzy sets. To express decision makers' perspectives on the truthiness (T), falsity (F), and indeterminacy (I) for a fuzzy set concurrently, this paper expands the usual neutrosophic TOPSIS approach to interval-valued neutrosophic. One example of how the suggested strategy might be put to use is to prioritize initiatives in the realm of corporate social responsibility using a combination of expert opinion and objective criteria.

The aim of this paper is to solve the problem of representing refined neutrosophic matrices by linear functions, where it describes the structure of refined neutrosophic linear transformations that represent refined neutrosophic matrices. On the other hand, this work introduces a novel algorithm to compute a basis of any refined neutrosophic vector space depending on the classical basis of its corresponding classical vector space.

Investors have been flocking to the information technology (IT) industry recently. Any commercial or IT company's success is directly proportional to its employees' efforts. The workforce's contributions are crucial when it comes to the success of technology or any other business on the global stage. However, they will disregard their personal and social lives to achieve their aim. Workers in the private sector, particularly those in the information technology industry, suffer from mental health issues such as stress, depression, anxiety, and addiction. Using Neutrosophic Cognitive Maps (NCM), we evaluated the daily problem they face. The NCM decision-making system incorporates iterative tasks of resolving conflicts until the optimal answer is reached. The NCM uses neutrosophic graphs to model depending on the opinions of experts. Studying the issue with such vague data calls for an approach such as this, which eschews the use of statistics. For unlabeled data, NCM is the most effective method.

Among the most valuable AI methods for modeling complicated things at the moment is the use of fuzzy cognitive mapping (FCMs). Conventional FCMs, on the other hand, can't handle the ambiguity that often arises in decision-making scenarios. A novel expansion of conventional FCMs called neutrosophic cognitive mapping (NCMs) was developed to address this shortcoming. However, the indeterminacy is not well handled by the NCMs stated in the citations since the level of indeterminacy is not quantified. In certain cases, choices should be seen as a series of steps that are only loosely related to one another. This occurs in project assessment when several activities depend on one another. Another difficult aspect of FCMs is that there isn't an appropriate topology for representing these types of decision-making difficulties. To aid in making decisions over several time periods, this research introduces a neutrosophic cognitive map built on triangular neutrosophic values (MS-TrNCM) for violence analysis. Through the use of triangular neutrosophic numbers, the suggested model allows experts to express their choices while considering various extents of truth, indeterminacy, and falsity in the underlying map linkages.

The Indonesian rolling stock maker's target market and business strategy are analyzed here—the study's planning, data, and technique. To achieve sustainable growth across the board in the power generating industry, we concentrate on understanding the critical variables driving sustainable development in a market context unlike before. To identify the most vital aspects to consider while dealing with ambiguous rules, a methodology using Multiple-Criteria Decision-Making (MCDM) was presented. To address ambiguity and bring the problem-solving process closer to reality, we created a unique method that integrates MCDM techniques. Analytical Hierarchy Process AHP was employed in this investigation. To zero in on our ideal clientele, we turned to the AHP technique. This strategy considers quantitative aspects such as market characteristics and degree of competition when making decisions. The results indicate that rolling stock manufacturers have good reason to invest in expanding their share of these markets. However, despite the many prospects available in this field, the rolling stock producer faces a significant obstacle: the inability to adequately fund the pursuit of a more considerable portion of the market

The Likert scale is by far the most popular psychometric tool for collecting data. The ordinal structure and confined style of the Likert scale make it prone to information misinterpretation and loss. Depending on the consumers' moods, replies in the real world are sometimes erratic, imprecise, and ill-defined. Neutrosophy (the study of the implementation of the provisions and indeterminacy) is utilized to accurately portray the answers. This work introduces a neutrosophic-informed, agnostic version of the Likert scale. Clustering users based on their comments is an efficient method of segmenting the population and marketing to them. In this research, we offer a clustering approach for responses received using arbitrary Likert scales. When dealing with real-world events, indeterminate Likert scales are superior in recording replies properly.

Recently, industrialization has led to a worldwide rise in energy usage. Consequently, satisfying rising energy demands has assumed more significance. Fuel, gasoline, and nat gas are all finite resources, making it all the more important to discover sustainable energy alternatives. To fulfill the current need for energy, renewable resources play a significant role. Therefore, energy decisions and government policy are of paramount importance for nations. Energy policy and judgment challenges, such as the appraisal of energy projects, the choice among fuel sources, the location of power plants, and the determination of energy policy, are solved using a variety of technical, financial, ecological, and social factors. Multi-criterion decision-making (MCDM) methodologies may be used to assess energy policy decisions, one of the important challenges for governments. Some of the challenges associated with making energy-related decisions and formulating policies are choosing between various energy sources, assessing the relative merits of various energy supply techniques, formulating an energy strategy, and carrying it through. Various forms of fuel sources are taken into account in the much research that has been conducted on energy decision-making challenges. Because they take into account several, sometimes competing, criteria in their assessments of potential solutions, MCDM techniques have proven useful in the resolution of energy-related decision-making issues. By combining MCDM with the neutrosophic set theory (NST), which captures the inherent ambiguity of human judgment, we may get more nuanced, tangible, and practical outcomes. This work intends to provide a thorough analysis of the methodology and implementations of neutrosophic MCDM in the power industry, as well as to synthesize the current literature and the latest recent breakthroughs to help guide researchers in this area. The neutrosophic Analytic Hierarchy Process (AHP) method is used to compute the weights of each criterion of energy in a social project. This research shows that neutrosophic AHP, either on its own or in combination with another MCDM approach, is the most often used MCDM technique.

Markets may be broken down into subsets with the use of cluster analysis. Multivariate analytic methods are often used in traditional research. Due to their success in engineering, artificial neural systems have recently found use in business as well. When it comes to grouping observations with comparable traits or attributes, the K-means method is a common choice. It has various uses in marketing, but it finds particular success in cluster analyses of customer behavior. Several commercial packages include implementations of the K-means algorithm. Data mining statistical approaches like K-Means are useful for handling this data and analyzing it later on. For better results, this study combines the traditional K-Means technique with Neutrosophy, which accounts for the uncertainty inherent in such complicated data sets by factoring in the data's diversity and its inherent volatility as a result of proximity between the bounds of the separate segments as well as the members who make up each.

This paper is dedicated to studying the neutrosophic formula of some famous matrix equations used in theoretical data mining algorithms and control systems by using neutrosophic matrices and refined neutrosophic matrices over neutrosophic real fields. On the other hand, we concentrate on the neutrosophic formula of the Sylvester equation, and Lyapunov equation, where we study their formulas and properties in terms of theorems in the neutrosophic real number field and refined real number field. Also, we illustrate many different examples to clarify the validity of our work.