International Journal of Neutrosophic Science

This study investigates the finite-time stability (FTS) of the discrete Sel’kov-Schnakenberg reaction-diffusion (SSRD) system, a mathematical model capturing the interplay between local reactions and spatial diffusion. A novel discretization framework based on finite difference methods (FDM) is developed to transform the continuous reaction-diffusion (RD) system into a discrete counterpart, enabling detailed computational analysis. Sufficient conditions for FTS are derived using Lyapunov functions (LF) and eigenvalue-based methods, ensuring precise predictions of the system’s behavior. Numerical simulations validate theoretical findings, demonstrating the proposed methods’ practical applicability to scenarios such as chemical reactions, biological processes, and technological systems. The influence of system parameters, boundary conditions, and initial conditions on the dynamic behavior is systematically analyzed. This study contributes to the broader understanding of RD systems, addressing key challenges in stability analysis and offering a computationally efficient framework with implications for science and engineering.

In this work, subsequent expansions of the operators , algebraic sum and geometric product over IVTNFs. The first of  is called the shrinking operator and the second, which is an extension of the first, is called  - shrink operator. The membership values & the values of non-membership be not completion our for all time possible, although in the branch of IVTNFS, it plays an additional significant character at this time, since the interval valued temporal neutrosophic fuzzy sets provides the best solution for finding the shortest distance in deciding one's career, judgment making and image processing and many more areas. Especially in medical diagnosis, when using this concept, there is a real chance that there will be a non-zero fraction of hesitation at any point in the assessment.

This work focuses on the estimation reliability function    where x and y are two independent Benktander distributions. The greatest likelihood's asymptotic distribution is found. The maximum likelihood estimator, the moment method estimator, and the approximate maximum likelihood estimator of are proposed. We obtain the asymptotic distribution of s maximum likelihood estimate. The  confidence interval can be found using the asymptotic distribution.

Fuzzy sets and probabilistic methodologies have been integrated with forecasting but do not simultaneously capture the truth, indeterminacy, and falsity—really the crux of Neutrosophic Logic (NL). There is no literature investigating the incorporation of neutrosophic numbers into deep architectures, in particular into Neutrosophic Neural Networks (NNNs) for demand forecasting. This contribution fills the gap with the presentation of a Neutrosophic Neural Network (NNN) model with uncertainty explicitly included, enhancing the reliability and explain ability of demand forecasting. Deep learning-based demand forecasting strategies involving the use of Random Forest regression and XGBoosting algorithms generally do not deal with uncertainty and imprecision related with real-world demand data. The current work introduces a new model Neutrosophic Neural Network (NNN) where Neutrosophic Logic (NL) is integrated into deep learning demand forecasting. A novel neutrosophic activation function and a Neutrosophic Mean Squared Error (NMSE) loss function are proposed study, is implemented with the Random Forest regression and XGBoosting algorithms, and trained using synthetic and real-world demand data. Experimental results establish the better performance of the NNN approach about forecasting accuracy, robustness, and uncertainty handling. The sensitivity analysis also confirms the flexibility of the model with different demand patterns. The work contributes significantly towards neutrosophic deep learning and the possibility of robust and interpretable demand forecasting for supply chain and business intelligence.

HXDTRU is a multidimensional public key encryption system with sixteen encrypted data vectors at each step. In this work, we propose HXDHS, an improved version of HXDTRU based on hexadecnion algebra with neutrosophic integer coefficients, as well as a new mathematical construction includes three private keys with one public key to enhance the security and robustness of the public-key system. HXDHS is suitable for applications that require concurrent operation from multiple sources.

This study evaluates the influence of technology risks on insurance company performance through Insurtech innovation, focusing on the roles of Data Privacy (DP), Skill Gaps (SG), and Financial Risks (FR) in predicting Insurance Performance (IP). Employing a questionnaire survey approach, the research extended historical empirical studies, capturing demographic profiles and study variables measured on a 5-point Likert scale. A pilot study refined the questionnaire, achieving an 80% response rate, and minor adjustments were made to enhance clarity. The dataset included 243 responses from employees of Jordanian insurance companies, with 37 excluded due to incomplete data. Validity and reliability were assessed using Average Variance Extracted (AVE), Composite Reliability (CR), and Cronbach's Alpha, confirming the robustness of the measurement model. Multicollinearity was tested using correlation, Tolerance, and Variance Inflation Factor (VIF), with no significant issues detected. ANOVA tests were conducted to examine the impact of experience and technology level on DP, SG, FR, and IP, revealing significant differences across groups. A multiple regression model demonstrated that DP and FR positively affect IP, while SG has a negative effect. To further predict IP, the dataset was split into 80-20% and 60-40% training-test sets, and a Multilayer Perceptron (MLP) model was employed. The MLP neural network model, using the Rprop method, highlights the importance of DP, SG, and FR in predicting IP, achieving an accuracy of up to 72%. These findings highlight the importance of addressing technology risks and leveraging Insurtech innovations to enhance insurance company performance, providing valuable insights for industry stakeholders and policymakers.

This paper presents four new types of continuity in the context of supra-soft topological spaces: supra-soft ω- continuity, supra-soft ω-irresoluteness, supra-soft contra-continuity, and supra-soft contra-ω-continuity. The main contribution is the clear definitions and detailed study of these concepts, which helps us better understand how they work and how they are interconnected. We carefully examine how these new concepts connect among themselves and with analogous concepts in traditional supra-topological spaces. We also demonstrate how these different forms of continuity behave under common mathematical operations, such as composition and restriction. To make everything easier to understand, we introduce several examples that emphasize how these new concepts compare with existing, well-known concepts, giving a better picture of how continuity works in a more generalized topological settings.

A hyperfunction maps each input to a subset of outputs, generalizing classical functions to represent multi-valued or uncertain outcomes. A superhyperfunction extends this idea further by mapping sets (or sets of sets) to higher-order powerset values, thereby capturing complex hierarchical or layered uncertainties. In this paper, we explore the use of hyperfunctions and superhyperfunctions in linear programming. Specifically, we examine the Linear Objective (Profit/Cost) n-SuperHyperfunction and the Linear Utility n-SuperHyperfunction. We hope these concepts will advance both hyperfunction theory and the study of linear programming under uncertainty.

This paper focuses on the stability of Descriptor Predator-Prey economic system and its related neutrosophic system of Holling type-III functional action response with harvested predator under classical real environment and neutrosophic environment. Where the solvability and dimensionless forms have been presented along with the necessary mathematical justifications and proofs with some qualitative properties have been proposed and developed with systematic illustration.

The main purpose of this paper is to define the notion of neutrosophic based normal and regular spaces. This study investigates and open new class and conception of generalization of classical regular and normal spaces. The hereditary and topological properties of neutrosophic based normal and regular spaces have been analyzed and investigated. It also examines neutrosophic topological subspaces, providing insights into their characteristics. Furthermore, the paper investigates neutrosophic regular spaces and demonstrates their hereditary nature, specifically focusing on R_1, R_2, R_3 and R_4. Additionally, we explain some example of a neutrosophic-regular based space X which is a neutrosophic based normal-space but it is not necessary to neutrosophic -〖T〗_1 spaces. Eventually, it is shown that under certain conditions that the images are preserved in neutrosophic based normal and regular spaces.

Multidimensional data cubes are essential components in data warehouses, enabling rich, OLAP-based analysis across dimensions such as time, location, and product category. However, the complexity that supports such analytical flexibility often leads to extreme sparsity—where the majority of cube cells remain empty or only partially filled. This sparsity can hinder the performance of downstream machine learning models, especially when valuable but infrequent patterns are lost during preprocessing. This paper introduces a neutrosophic-based framework for evaluating and managing sparse regions within OLAP cubes. Instead of treating all sparsity as noise, we propose a typology that distinguishes between three forms: semantic sparsity (expected and justifiable absences), non-informative sparsity (regions with little analytical value), and informative sparsity (sparse areas that still carry meaningful insights). Each substructure is modeled using neutrosophic logic, which assigns degrees of truth, indeterminacy, and falsity to reflect its analytical potential. A dedicated Neutrosophic Evaluation Algorithm is developed to classify each region using metrics such as semantic confidence, entropy, and a context-aware informativeness score. These metrics allow for nuanced decisions: preserving informative sparsity, eliminating irrelevant regions, and flagging ambiguous areas for further review. This approach shows how neutrosophic logic can offer a novel and effective way to handle sparsity in OLAP cubes, improving the relevance and robustness of machine learning pipelines trained on multidimensional data.

This paper proposes a novel smart farming decision-making framework that integrates machine learning (ML) techniques Support Vector Machine (SVM), Fuzzy C-Means (FCM) clustering, with the generalized distance and similarity measures in a linguistic neutrosophic hypersoft set environment. ML processes real-time sensor data to predict weather patterns, while linguistic neutrosophic terms capture uncertainty, indeterminacy, and falsity, allowing for a more precise analysis of imprecise information. Through the application of generalized similarity measures, the framework ranks the cities suitable for farming strategies based on multiple criteria such as temperature, wind speed, and humidity. The use of linguistic neutrosophic terms offer enhanced flexibility in managing weather-related uncertainty compared to existing methods. The outcomes demonstrate that this integrated approach optimizes decision-making under uncertain environmental conditions, enabling more efficient resource management and improving resilience in farming practices. Future research will further explore the inclusion of additional environmental factors and improve similarity measures to increase decision accuracy among broader agricultural contexts. This model also has the potential to be applied to other domains where uncertainty management is crucial, such as climate resilience and environmental sustainability.

Let  be the direct product of an associative ring . In the work the concepts of Endo Bi-Antiderivation, Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation on a ring  are introduced, furthermore the relations between these bi-additive mappings are given. As essential point, we searched for appropriate conditions that make equivalence between Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation. Also, we prove the same results for the generalized case of neutrosophic rings.

Starting from semi-explicit perturbed bilinear time varying neutrosophic differential – algebraic equations (PBTVDAs). We develop a method for the stabilization of this controlled bilinear time varying neutrosophic differential – algebraic equations and prove that the controlled perturbed system can be stabilized by putting specific conditions on the proposed control. This method transfers the system to standard canonical form and uses the exponential stability concept. Therefore, the stabilization of this system is achieved finally; we present numerical results for the battery model, which confirm the theoretical results.

This paper is dedicated to study for the first time the applications of neutrosophic BDF and CDF Newton's methods for finding the numerical solutions of some different problems related to the derivations from first and second order applied on neutrosophic-tabulated functions, where we apply those novel methods on some problems and list the solutions by using the numerical tables. In addition, we provide a theoretical discussion and description of these methods to be applicable on other numerical problems.