International Journal of Neutrosophic Science

Due to the increase in violence in Ecuador involving juvenile offenders, an analysis of the situation is proposed from a neutrosophic approach to address the violation of due process in adolescents in Ecuador, highlighting the importance of considering the complexities and ambiguities of the juvenile penal system. Challenges are identified and classified through the PESTEL technique related to legal deficiencies, economic constraints, and socio-environmental factors contributing to juvenile delinquency, which are processed hermeneutically in a TOPSIS that uses single-valued neutrosophic numbers. The processing's main outcome is the influence of legal and economic aspects, thus the need to promote legal reforms, strengthen institutional capacities, invest in preventive programs, and support social reintegration and the responsible use of information technologies. The conclusions emphasize the importance of a comprehensive and coordinated approach to improve juvenile justice in Ecuador, ensuring respect for due process and the rights of adolescents.

The notion of neutrosophic m-polar fuzzy sets is much wider than the notion of m-polar fuzzy sets. In this paper, we apply the theory of neutrosophic m-polar fuzzy set on UP-algebras. We introduce the concepts of neutrosophic m-polar fuzzy subalgebras, neutrosophic m-polar fuzzy ideals and neutrosophic m-polar fuzzy strong ideals and some essential properties are discussed. We characterize neutrosophic m-polar fuzzy subalgebras in terms of fuzzy subalgebras and subalgebras of UP-algebras.

In this paper, we propose a novel combination of the (He) method with (Mohand transform), and this combination is summarized by representing the nonlinear part (or the residue of the operator) with (He) polynomials after applying the Mohand transform. To prove the accuracy of the proposed method, we applied it to several neutrosophic partial differential equations such as neutrosophic version of Helmholtz equation, neutrosophic version of non-linear oscillator, neutrosophic version of Burger's equation, and the neutrosophic version of telegraph equation. The accuracy and effectiveness of the application of the proposed method was verified by comparing the results obtained with other methods using the Maple software package.

The transportation problem has received a lot of attention in the field of operations research. In many circumstances, transportation planners may lack clear information on supply, demand, and transportation costs. Fuzzy sets can accept incomplete information by allowing for degrees of membership, which describe the level of certainty or uncertainty associated with each parameter. Three components—truth-membership, indeterminacy-membership, and falsity-membership degrees—are added to fuzzy numbers to create neutrosophic fuzzy numbers, which enables a more complex depiction of uncertainty. In this paper, we discuss the fuzzy transportation problem in a neutrosophic environment. Here the transportation costs, demands, and supplies are represented by neutrosophic trapezoidal fuzzy numbers. The neutrosophic trapezoidal fuzzy numbers are transformed into crisp numbers by using a ranking function and providing numerical examples to show the proposed method's efficiency to get the minimum optimal cost. Finally, we have demonstrated that our proposed method produced a better optimal solution to existing approaches by comparing its results to those of the existing ones.

This article presents a new way of analyzing multiple attribute decision-making (MADM) using (♭1, ♭2, ♭3) sin trigonometric complex neutrosophic sets (ST-CNS). Complex neutrosophic weighted averaging (ST-CNWA), sin trigonometric complex neutrosophic weighted geometric (ST-CNWG), sin trigonometric complex generalized neutrosophic weighted averaging (ST-CGNWA), and sin trigonometric complex generalized neutrosophic weighted geometric (ST-CGNWG). During our discussion, we presented an algorithm that utilized these operators. There are extensive numerical illustrations of score values. Furthermore, we will discuss commutativity, idempotency, and monotonicity of sin trigonometric complex neutrosophic sets as part of our discussion. It is easier, faster, and more convenient to find the best option this way. Consequently, the sin trigonometric complex (♭1, ♭2, ♭3) is more closely related to precise conclusions. Also revealed by the study was an intriguing and fascinating observation.

In this article, we present the notion of Single-Valued Pentapartitioned Neutrosophic Bi-Topological Space (SVPNBTS) as a generalization of Single-Valued Pentapartitioned Neutrosophic Topological Space (SVPNTS) and Neutrosophic Bi-Topological Space (NBTS). Besides, we study the different types of open set and closed set namely single-valued pentapartitioned neutrosophic bi-open set (SVPNBOS), single-valued pentapartitioned neutrosophic bi-closed set (SVPNBCS), single-valued pentapartitioned neutrosophic bi-semi-open set (SVPNBSOS), single-valued pentapartitioned neutrosophic bi-semi-closed set (SVPNBSCS), single-valued pentapartitioned neutrosophic bi-pre-open set (SVPNBPOS), single-valued pentapartitioned neutrosophic bi-pre-closed set (SVPNBPCS), single-valued pentapartitioned neutrosophic bi-b-open set (SVPNBb-OS), single-valued pentapartitioned neutrosophic bi-b-closed set (SVPNBb-CS), etc. via SVPNBTSs. Besides, we introduce the notion of pairwise SVPNOS, pairwise SVPNCS, pairwise SVPNSOS, pairwise SVPNSCS, pairwise SVPNPOS, pairwise SVPNPCS, pairwise SVPNb-OS, pairwise SVPNb-CS, and furnish few illustrative examples on them. Further, we investigate several properties of these classes of sets and prove some interesting results in the form of propositions, theorems, etc. via SVPNBTSs.

This research introduces the Neutrosophic Vendor-Buyer Economic Order Quantity (EOQ) model, integrating Neutrosophic Set Theory and Particle Swarm Optimization (PSO) for advanced inventory management. Addressing uncertainties in demand and costs, Neutrosophic Sets quantify truth, indeterminacy, and falsity degrees for key parameters. The model, employing PSO inspired by collective behaviour in nature, aims to minimize the combined total cost (C) encompassing vendor and buyer expenses. A grocery store scenario illustrates the approach, demonstrating substantial total cost reduction through the optimization of decision variables. MATLAB R2015a visualizations include a mesh plot depicting cost changes across varying EOQ and demand variability values, emphasizing optimal solutions. A bar chart compares initial and optimized total costs, showcasing efficiency gains. Cost breakdowns and pie charts detail the impact on vendor and buyer expenses. Sensitivity analysis systematically explores variable influences, aiding decision-makers in understanding trade-offs and optimal ranges by using Python. This comprehensive framework contributes empirical insights for practical implementation, enabling businesses to make informed decisions and enhance adaptive inventory strategies efficiently.

This study employs a Pythagorean Neutrosophic Bonferroni Mean (PNBM) - Decision Making Trial and Evaluation Laboratory (DEMATEL) approach to analyze barriers faced by young entrepreneurs in Digital Social Innovation (DSI). Pythagorean Neutrosophic Set (PNS) enriches the analysis, accommodating uncertainties in the complex socio-economic context. Limited Access to Funding emerges as the most influential barrier, showcasing its pivotal role in impacting other DSI challenges. Regulatory and Compliance Challenges are identified as interdependent, emphasizing their interconnected nature with broader barriers. Neutrosophic elements elucidate the uncertainties surrounding financial constraints, regulatory frameworks, and mentorship dynamics. The study contributes to a nuanced understanding of DSI challenges and pioneers the application of neutrosophic logic in socio-economic research. It advocates for a more inclusive decision-making methodology, fostering adaptability in addressing the indeterminate nature of barriers faced by young entrepreneurs navigating the digital social innovation landscape. The findings aim to enhance support systems, fostering a conducive environment for DSI initiatives and encouraging future research in neutrosophic decision-making methodologies.

The current work offers a new concept of sets and called uzzy eutrosophic m-closed sets in fuzzy neutrosophic topology. In fact, the research is an extended form of a research conducted by F. M. Mohammed et.al. [1-7]. It explores a number of noteworthy examples to shed the light on the new characteristics and attributes of these recently formed conceptions, as well as some associated interactions between them.

The significance and influence of neutrosophic crisp set theory in numerous scientific domains, particularly topology, led us to construct a new definition of topology based on neutrosophic crisp sets, allowing us to regulate its key mathematical ideas. Therefore, we constructed this definition and dubbed it stable neutrosophic crisp topology, where we went over the key idea which is the interior with the vital features.

A new approach to multiple attribute decision-making (MADM) is presented in this article, which is based on (ȷ1, ȷ2, ȷ3) complex neutrosophic sets (CNS). We are extending the CNS in this way. Complex neutrosophic weighted averaging (CNWA), complex neutrosophic weighted geometric (CNWG), complex generalized neutrosophic weighted averaging (CGNWA), and complex generalized neutrosophic weighted geometric (CGNWG). An algorithm utilizing these operators was presented during our discussion. Extensive score and accuracy values are illustrated numerically. We will also discuss idempotency, boundedness, commutativity, and monotonicity of complex neutrosophic sets as part of this communication. You can find the best option faster, easier, and more conveniently with them. Therefore, complex (ȷ1, ȷ2, ȷ3) is more closely associated with more precise conclusions. A fascinating and intriguing finding was also revealed by the study.

The objective of this paper is to investigate the innovative concept of complex neutrosophic subbisemiring. The novelty of the complex neutrosophic subbisemiring lies in its wide range of truth, indeterminacy, and false function values. It goes beyond the range of [0,1] in the complex plane in contrast to the traditional range [0,1]. Therefore, these three functions can be described mathematically using a complex number in the complex neutrosophic subbisemiring. We develop and analyze the concept of complex interval-valued neutrosophic subbisemiring (CIVNSBS). Moreover, we study homomorphic characteristics and important properties of CIVNSBS. We propose the level sets of CIVNSBS and complex interval valued neutrosophic normal  subbisemiring (CIVNNSBS) of bisemirings. Moreover, we introduce CIVNNSBS of bisemiring. Let ¡ be a complex neutrosophic subset of bisemiring S. Then is a CIVNSBS of S if and only if all non empty level set  is a subbisemiring, where . Let ¡be a CIVNSBS of bisemiring S and V be the strongest complex neutrosophic relation of bisemiring S. Then  ¡ is a CIVNSBS of bisemiring S if and only if V is a CIVNSBS of . We illustrate that homomorphic images of every CIVNSBS is a CIVNSBS and homomorphic pre-images of every CIVNSBS is a CIVNSBS. Examples are provided to illustrate our results.

Leukemia recognition and classification contain the identification of dissimilar kinds of leukemia, a group of blood cancers that affects the bone marrow and blood. A classical model containing microscopic analysis of blood smears to classify abnormal cells analytic of leukemia. Leukemia recognition employing a united technique of neutrosophic logic and deep learning (DL) signifies a new and complete approach to handling uncertainty and difficulty in medical data. Neutrosophic logic permits the representation of unstated or imperfect data, which is general in medical analyses. DL mainly convolutional neural networks (CNN) or recurrent neural networks (RNN), which can mechanically remove difficult patterns from medicinal imageries, improving the accuracy of leukemia recognition. The neutrosophic logic module accommodates the characteristic uncertainty in medicinal data, offering a formalism to manage imperfect or inaccurate data linked with the analysis procedure. The combination of these dual techniques generates a robust structure which capable of leveraging both the control of DL in image analysis and the flexibility of neutrosophic logic in dealing with uncertainties, contributing to more trustworthy and interpretable leukemia recognition methods.  This study develops a new Salp Swarm Algorithm with a Neutrosophic Logic SVM (SSA-NSVM) model for Leukemia Detection and Classification. The SSA-NSVM technique mainly exploits Neutrosophic Logic (NL) concepts with the DL model for the detection of leukemia. To attain this, the SSA-NSVM model uses bilateral filtering (BF) based image pre-processing. In addition, the SSA-NSVM approach applies a modified densely connected networks (DenseNet) technique for learning complex and intrinsic feature patterns. Besides, the hyperparameter range of the modified DenseNet system takes place utilizing a SSA. At last, the NSVM technique is employed for the detection and identification of leukemia. The performance validation of the SSA-NSVM algorithm is verified utilizing a benchmark medicinal image dataset. The simulation values emphasized that the SSA-NSVM model reaches better detection outcomes than other existing approaches.

A soft expert set is a concept that combines elements of soft sets and expert systems. It aims to incorporate expert knowledge and uncertainty-handling capabilities into the analysis and decision-making processes. On the other hand, the idea of single neutrosophic sets (SVNSs) and fuzzy sets (FSs) are imported models for handling the uncertainty data. In this work, the authors combine the critical features of FSs and SVNSs under expert systems in one model. Accordingly, this model worked to provide decision-makers with more flexibility in the process of interpreting uncertain information. From a scientific point of view, the process of evaluating this high-performance SVNFSES disappears. Therefore, in this paper, we initiated a new approach known as single-valued neutrosophic fuzzy soft expert sets (SVNFSESs) as a new development in a fuzzy soft computing environment. We investigate some fundamental operations on SVNFSESS along with their basic properties. Also, we investigate AND and OR operations between two SVNFSESS as well as several numerical examples to clarify the above fundamental operations. Finally, we have given distance measures (DM) between two SVNFSESs to construct a new algorithm that is used to demonstrate the effectiveness of the method in handling some real-life applications.

The focus of operations research is the existence of a problem that requires making an appropriate decision that helps reduce risk and achieves a good level of performance. Operations research methods depend on formulating realistic issues through mathematical models consisting of a goal function and constraints, and the optimal solution is the ideal decision, despite the multiplicity of these methods. However, we encounter many complex issues that cannot be represented mathematically, or many issues that cannot be studied directly. Here comes the importance of the simulation process in all branches of science, as it depends on applying the study to systems similar to real systems and then projecting this. The results if they fit on the real system. So simulation is the process of building, testing, and running models that simulate complex phenomena or systems using specific mathematical models. The simulation process depends on generating a series of random numbers subject to a regular probability distribution in the field [0, 1], and then converting these random numbers into random variables subject to the distribution law. Probability, according to which the system to be simulated operates, using appropriate techniques for both the probability density function and the cumulative distribution function. Classical studies have provided many techniques that are used during the simulation process, and to keep pace with the great scientific development witnessed by our contemporary world, we found that a new vision must be presented for this. Techniques A vision based on the concepts of neutrosophics, the science founded by the American mathematical philosopher Florentin Smarandache. The year 1995, in which new concepts of probabilities and probability distributions are used, as we presented in previous research some techniques from a neutrosophic perspective, and as an extension of what we presented previously, we present in this research a neutrosophic vision of the Box and Muller technique used to generate random variables that follow a normal distribution.