The study of logic mining has gained significant attention for its ability to interpret behavior of the datasets. However, existing logic mining models face limitations such as reliance on single optimal logic, insufficient focus in attribute selection methods and a tendency to overfit especially when dealing with imbalanced datasets. To address these challenges, this paper introduces a versatile and flexible logic mining model based on Conditional Random 2 Satisfiability. The proposed model is structured into three main phases: pre-processing, learning and retrieval. By utilizing a multi-objective retrieval phase, the model improves its classification performance by retrieving a final neuron state that is optimally diversified. A different pathway in generating the best logic expands the search space leading to the production of a set of induced logics using different confusion matrixes. As a result, the logic mining model moves beyond a rigid dependency on the single best logic and thus offers flexibility in interpreting the behavior of the datasets. Additionally, the similarity analysis enhances the attribute selection method by calculating the distance between attributes and dataset outcomes. This evaluation considers the distribution of both positive and negative entries across independent and dependent attributes. Comparative experiments conducted on real-world datasets demonstrate the superiority of the proposed logic mining model, achieving an average ACC = 0.8275, PRE = 0.9116, SPE = 0.9994, MCC = 0.5221 and MCR = 0.1758. These results consistently outperform baseline logic mining models across all evaluation metrics.

The Boolean 3-Satisfiability (3-SAT) problem is widely recognized as a canonical NP-complete problem with broad applications in artificial intelligence, circuit design, and cryptography. Discrete Hopfield Neural Networks (DHNNs) have demonstrated potential for addressing this challenge due to their associative memory properties and parallel dynamics. However, classical DHNN-based 3-SAT models typically rely on complex higher-order synaptic weight computations, which severely limit scalability and computational efficiency in large-scale instances. To overcome these limitations, this study proposes a more scalable and computationally efficient DHNN-based framework for solving the 3-SAT problem. Specifically, the proposed framework introduces a simplified method based on a reformulated cost function that enables the direct encoding of clause-level logical structures while avoiding explicit high-dimensional tensor operations. As a result, both computational overhead and memory requirements are significantly reduced. Experimental results demonstrate improved learning and retrieval times, reduced memory consumption, and consistently high retrieval accuracy across both small-scale and large-scale 3-SAT instances. These improvements enhance the practical applicability of DHNN-based models in logic programming and combinatorial optimization, particularly for large and structurally complex problem settings.

This work presents a space-time variable-order (V-O) fractional framework for the analytical investigation of nonlinear longitudinal wave propagation in magneto-electro-elastic (MEE) materials. The model contains Caputo-type V-O derivatives, which account for spatial and temporal memory effects and nonlocal interactions inherent to coupled mechanical, electrical, and magnetic fields. On this basis, exact traveling-wave solutions of the resulting nonlinear fractional wave equation were derived using an exponential expansion methodology, in the form of periodic, kink-type, and solitary waves. The effect of the V-O parameters on the wave amplitude, dispersion characteristics, and stability behavior is systematically analyzed. Stability and bifurcation analyses show parameter-dependent transition of both stable and unstable regimes, whereas insertion of random perturbations illustrates the development of chaotic dynamics. The proposed V-O model offers increased modeling flexibility and parameter-dependent stability regimes in the reduced system compared to constant-order (C-O) fractional formulations. This enhancement provides increased analytical flexibility at the theoretical level for coupled field interactions in MEE media. These results suggest that the V-O fractional modeling represents a valid tool for the analysis of complex nonlinear electromechanical phenomena and could lead to a better understanding of the wave dynamics at a theoretical level in multifunctional material systems.

A deeper understanding of the learning and retrieval phase of the Discrete Hopfield Neural Network (DHNN) is essential for advancing its application in intelligent systems. This study investigates the performance of a non-systematic logical rule, namely Conditional Random 2 Satisfiability logic (CRAN2SAT) in DHNN (DHNN-CRAN2SAT) in retrieving diverse and optimal final neuron states. The findings show that the Election Algorithm consistently retrieves the maximum global minimum solution value of 1 across all tested neuron sizes, outperforms Exhaustive Search. In addition, the implementation of a new updating rule during the retrieval phase significantly enhances the diversity of final neuron states. This improvement is reflected by lower Sokal–Sneath similarity indices with an average value of 0.3809 and increased neuron state variation with an average value of 8809. These results highlight the significance of both the learning algorithm and updating strategy in the retrieval phase of DHNN. By enabling a broader range of final neuron states, this approach offers meaningful improvements for logic mining models, particularly in addressing real-world classification challenges.

The random Boolean satisfiability (SAT) problem is a fundamental NP-complete problem characterized by high-dimensional search spaces and complex energy landscapes. This study proposes DHNN-RAN3SAT-KMIEA, an enhanced Discrete Hopfield Neural Network (DHNN) framework for solving mixed 2-SAT/3-SAT instances. The model integrates K-Medoids clustering to structure the initial solution space through Hamming-distance partitioning, coupled with an Improved Evolutionary Algorithm (IEA) incorporating adaptive mutation, crossover, and elitism to strengthen global exploration and reduce premature convergence. Logical clauses of variable length are encoded using the proposed WA-BBLV weight computation scheme, and a block-based incremental update mechanism is introduced to lower computational cost during dynamic clause modifications. Experimental results on SATLIB JNH benchmarks demonstrate statistically significant and consistent improvements over WA-, EA-, and MOHEA-based DHNN baselines across key optimization metrics including Global Minimum Ratio and Mean Convergence Time. These results confirm the scalability and superior optimization capability of DHNN-RAN3SAT-KMIEA for large-scale random SAT problems.

Nowadays, researchers are focused on enhancing the learning phase in Discrete Hopfield Neural Network, but little attention has been given to simultaneously improving both the learning and retrieval phases. This study aims to address this gap by optimizing not only the learning phase but also the final neuron state retrieved by the network. This is achieved through the implementation of an Election Algorithm as a learning algorithm and a Hybrid Binary Whale Optimization Algorithm for optimizing the retrieved neuron states. This contributes to the achievement of multiple objectives including maximizing diverse solutions while maintaining a maximum global solution and minimizing similarity index values. The effectiveness of the model in achieving these multiple objectives is compared to various baseline metaheuristic algorithms and it is demonstrated that the proposed model outperforms these baseline algorithms in successfully fulfilling the specified multi-objectives. The performance analysis of these baseline algorithms show that the proposed algorithm achieves a 100

Fractional diffusion models are widely used to describe anomalous transport phenomena but pose significant computational challenges due to their nonlocal temporal operators. In this work, we propose a high-order iterative grouping algorithm for the efficient numerical simulation of multi-dimensional fractional diffusion equations. The method combines a fourth-order finite difference discretization with a structured grouping strategy that reduces iteration counts and computational overhead while preserving numerical stability. The proposed algorithm is analyzed in terms of stability and convergence and is evaluated through a set of numerical experiments that assess accuracy, runtime, and computational efficiency on refined spatial-temporal grids. Performance results demonstrate that the grouping strategy significantly accelerates convergence compared to standard pointwise iterative methods, particularly for moderately refined grids and long-time simulations. The algorithm demonstrates strong computational efficiency on a single computing device. Due to its block-structured formulation, it has potential for parallel and distributed implementations; however, such HPC-oriented performance is not evaluated in the present study. The nonlocal temporal structure of fractional diffusion equations leads to high computational and memory demands for fine spatial-temporal discretizations, motivating the use of HPC for large-scale simulations.

In Hand, Foot, and Mouth Disease (HFMD) control, conventional SEIR/SIR models rely on static parameters, which limits their adaptability to dynamic real‑world conditions. To address this, we propose a SEIRQ–ARIMA hybrid model that integrates a quarantine‑enhanced SEIR framework (SEIRQ) with an ARIMA time‑series model, whose dynamic parameters are optimized via a multi‑stage Artificial Bee Colony–Grey Wolf Optimization (ABC–GWO) algorithm. This study contributes three key novelties to the field: (i) an IoT-driven dynamic SEIRQ parameterization with explicit intervention tracking via time-varying isolation rate δ(t); (ii) a multi-stage ABC–GWO calibration strategy that improves stability and mitigates premature convergence in nonlinear parameter estimation; and (iii) an interpretable SEIRQ–ARIMA fusion that combines mechanistic dynamics with statistical residual learning to support both accurate forecasting and policy-oriented evaluation. The core innovation is that, unlike traditional SEIR models that ignore quarantine interventions, our SEIRQ framework is designed to dynamically calibrate the isolation rate δ using real-time Internet-of-Things (IoT) surveillance streams. In this study, we validate the framework using historical surveillance records from Guangxi, China (2014–2020). the model achieves substantial forecasting improvements,reducing RMSE by 94.6% compared to the standalone SEIRQ model and reducing MAE by 94.1% compared to ARIMA.In practical application, this study provides the quantitative estimation of HFMD quarantine effects: at the optimal isolation rate (δ = 0.413), the infection peak is reduced by 52.7%, with an overall peak reduction of 40–65% and a cost–benefit ratio of 1:8.7. Sensitivity analysis identifies δ ∈ [0.3, 0.5] as a critical isolation range. Remaining limitations include simplified economic assumptions; future work will incorporate more detailed cost‑effectiveness modeling and Transformer‑based prediction modules.

Over the years and across various scientific fields, artificial neural networks (ANN) have achieved remarkable success. Among these is deep feedforward neural networks (FFNNs) which notably enhanced the accuracy of numerous tasks. Despite their capabilities, their potential for solving complex higher-order equations has not been extensively explored. This study introduces an innovative method to improve the accuracy and efficiency of solving third-order differential equations (ODEs) by combining a hybrid block method with feedforward neural networks (FFNNs). In this approach, neural networks which are a subset of neural computing, are utilized to develop a new solution technique for approximating third-order ODEs, leveraging advanced mathematical tools and neural-like computation systems. The hybrid block method divides the problem into manageable segments, while the FFNNs iteratively learn and refine the solutions. This combination harnesses the computational efficiency of block methods and the adaptive learning capabilities of FFNNs to enhance solution accuracy. We provide a detailed methodology for implementing this hybrid approach and validate its effectiveness through numerical experiments and comparisons with existing methods. The results indicate substantial improvements in accuracy and computational efficiency, suggesting that the proposed method is a promising tool for solving complex third-order ODEs in various domains.

This study examines the influence of the COVID-19 epidemic on the global stock market using mean-variance optimization (MVO) based on Markowitz's portfolio theory. The analysis examines the performance of portfolios tailored to different sectors both before, during and the post-pandemic. It provides insights into the changes in risk-return characteristics across diverse businesses. The dataset consists of the mean closing prices of a variety of stocks, divided into two/three separate periods: before the outbreak of COVID-19, during the COVID-19 and post-pandemic. The study utilizes covariance matrices, anticipated returns, and logarithmic returns to calculate efficient frontiers that emphasize portfolios with the highest Sharpe ratios. The results demonstrate substantial alterations in the relationship between risk and return in several industries, illustrating the diverse influence of the pandemic on themarket. The efficient boundaries clearly illustrate a significant change in the optimal weights and risk levels of portfolios, with certain sectors experiencing higher volatility and lower returns amid the epidemic. The study also does a back testing of the optimal portfolios, uncovering varying levels of performance and durability during the periods. These findings underscore the importance of implementing adaptive portfolio management strategies, particularly in the face of global crises such as COVID-19. In addition, the study performs a sensitivity analysis by altering important criteria such as the risk-free rate and the quantity of assets in the portfolios in order to assess the strength and reliability of the results. This research provides a more profound understanding of how changes in assumptions can impact portfolio performance and the selection of optimal choices. In summary, this research provides significant information for investors by offering a quantitative framework that can help in effectively managing portfolios during periods of market volatility. The study emphasizes the importance of employing adaptable investing strategies to minimize risks and maximize returns in the face of unprecedented problems such as the COVID-19 pandemic.

This study addresses the limitations of traditional Boolean-based methods for solving 2SAT problems, which mainly classify variables as true or false and struggle with imprecise information and local minima in Hopfield Neural Networks (HNN). To overcome this challenge, we developed a novel approach that integrates fuzzy logic with HNN, introducing flexibility by permitting the network to handle partial truths during the learning phase. To further enhance this approach, we incorporated Simulated Annealing (SA) and Modified Grey Wolf Optimization (MGWO) to improve the network's ability to escape local minima and find optimal solutions. We developed three hybrid models: HNN2SATFuzzy, HNN2SATFuzzySA, and HNN2SATFuzzyMGWO, and evaluated their performance using metrics such as RMSE, MAE, SSE, SMAPE, global minimum ratio, and computation time. The results show that HNN2SATFuzzyMGWO outperformed the other hybrids, offering a more robust, accurate, and efficient solution to 2SAT problems. This work extends the applicability of HNN in solving SAT problems and provides a sophisticated alternative to classical Boolean approaches, paving the way for more adaptable problem-solving techniques in this field.

Software quality evaluation (SQE) plays a critical role in software development, requiring decision-making across multiple factors. As decision-making scenarios become more complex, researchers have increasingly focused on group decision-making (GDM) models. Key tasks in GDM include determining expert weights and assessing the closeness between decision matrices. This study introduces a new GDM framework for multi-attribute decision-making using interval-valued intuitionistic fuzzy (IVIF) evaluation information. The proposed method begins with a novel normalized projection measure to evaluate the proximity between two IVIF matrices. Based on this measure, a technique is developed for calculating expert weights and enhancing the VlseKriterijumska Optimizacija Kompromisno Resenje (VIKOR) methodology. The framework integrates group utility, regret, and satisfaction measures, and is applied to a case study on SQE to evaluate its effectiveness through both static and dynamic experiments. A dynamic data testing approach is also introduced to further demonstrate the superior performance of the proposed framework. Results show that the method outperforms existing approaches in terms of robustness, stability, and comprehensiveness. The study’s findings provide valuable insights into software quality management and offer practical implications for organizational applications. Furthermore, the method’s applicability extends beyond SQE, offering new perspectives and benchmarks for decision-making research in diverse domains.

Changes in population and population dynamic modelling are essential for ensuring optimal resource allocation and sustain development towards guiding strategic planning. Approximately 33.9 million inhabitants can be counted as the current populations of Malaysia. The changes in populations are mainly attributed to fertility and mortality change rates, urbanization, migration, and other socio-economic factors. Most importantly, however, the annual rate of population growth decreased from one point two-five percent in 2019 to one point zero-six percent in 2024 due to the significant effect of COVID-19, which reversed or changed societal norms, increasing death rates, and created another kind of economic uncertainty. The traditional population estimation approaches, like exponential and logistic growth models, do not usually incorporate the complexity and nonlinearity associated with demographic trends. As a consequence, this research utilizes population data from the Macrotrends database for an exploration of advanced iterative numerical techniques, particularly the Newton-Raphson technique. The latter is famous for its computational efficiency, rapid convergence, and accuracy in solving nonlinear algebraic equations, and it may well serve as an attractive alternative in demographic forecasting techniques. However, its sensitivity to initial approximations and the need for derivatives are known limitations. In this study, the Newton-Raphson method is applied to Malaysian population data for the years 2019 to 2024 to predict the population count in 2025. The study thus fills a critical dogma in the application of numerical optimization techniques to demographic analysis by showing that the methodology holds promise of overcoming the shortcomings of the traditional models. Thus, it would be practically valuable and computationally efficient in modeling population growth, providing a robust base for designing simulators.

Unconstrained exposure of humans and their immediate environments to electrostatic fields generated by high-voltage transmission lines has raised a lot of concerns regarding public health safety. These transmission lines, often sited near human residential and urban areas, may pose long-term health risks depending on the strength and duration of exposure. Various studies have linked prolonged exposure to electromagnetic fields to various health conditions, including neuropsychological disorders, cardiovascular diseases, and central nervous system complications. While high-voltage transmission lines are essential for efficient power distribution, their proximity to populated areas necessitates regulatory policies to mitigate potential risks. This study aims to analyse the spatial variation and intensity of the electrostatic field distribution around high-voltage power transmission lines in Malaysia, using two numerical methods, considering the country’s infrastructure features and regulatory emphasis on public exposure limits. The Finite Difference Method (FDM) and the Crank-Nicolson Method (CNM) are applied to solve Laplace’s Equation, which governs electrostatic potential, field intensity and distribution. Factors such as voltage levels, tower configurations, and conductor height are considered in the analysis. The study compares the accuracy, convergence rate, computational efficiency, and execution time of both numerical techniques to determine which of the methods is more suitable to solve such a problem. Our result demonstrates that FDM is fundamentally more suited for solving the Laplace equation governing electrostatic potential, field intensity, and spatial distribution due to its direct discretisation of spatial derivatives while using CNM in this context only introduces unnecessary complexity and computational overhead without providing any benefits in returns. The study provides insights into safe management practices by identifying critical zones of elevated electrostatic field intensity, indicating minimum safe distances for human exposure, and supporting infrastructure planning in accordance with Malaysian regulatory standards.

In this article, we present an efficient and highly accurate numerical scheme that achieves exponential convergence for solving nonlinear Riesz distributed-order fractional differential equations (RDFDEs) in one- and two-dimensional initial–boundary value problems. The proposed method is based on a two-stage collocation framework. In the first stage, spatial discretization is performed using the shifted Legendre–Gauss–Lobatto (SL-G-L) collocation method, where the approximate solutions and spatial derivatives are expressed in terms of shifted Legendre polynomial expansions. This reduces the original problem to a system of fractional differential equations (FDEs) for the expansion coefficients. Then, the temporal discretization is achieved in the second stage via Romanovski–Gauss–Radau collocation approach, which converts the system into a system of algebraic equations that can be solved efficiently. The method is applied to one- and two-dimensional nonlinear RDFDEs, and numerical experiments confirm its spectral accuracy, computational efficiency, and reliability. Existing numerical approaches to distributed-order fractional models often suffer from poor accuracy, instability in nonlinear settings, and high computational costs. By combining the efficiency of Legendre polynomials for bounded spatial domains with the stability of Romanovski polynomials for temporal discretization, the proposed two-stage framework effectively overcomes these limitations and achieves superior accuracy and stability.

In this paper, the two-dimensional (2-D) fractional cable equation (FCE) with the Caputo variable-order (V-O) derivative was utilized for simulating systems with memory and hereditary characteristics that vary across time and space. This variable-order fractional model is particularly well suited for the description of neuronal dynamics in biological systems. The accurate modeling of dynamic, memory-dependent behaviors that vary over space and time, which are essential for applications such as neuronal dynamics, presents a challenge for conventional numerical methods. Furthermore, there is a lack of stable and effective numerical techniques for 2-D V-O systems, highlighting the need for improved computational approaches. In order to solve the cable equation numerically with high accuracy and computing efficiency, this work primarily focused on using a higher-order finite difference method. The proposed method's robustness was confirmed by stability and convergence analyses, while its efficacy was demonstrated by numerical simulations, which were presented in tabular and graphical formats. These findings demonstrate its precision and efficiency when dealing with the intricate dynamics of V-O fractional equations. The study concludes that the higher-order finite difference method offers an accurate and effective framework for solving fractional such as biological and physical systems. It also creates opportunities for future research, such as the application of the method to multivariate problems, the integration of machine learning techniques, or the adaptation of the method to systems with variable coefficients.

This article explores recent advances in integrating artificial neural networks (ANNs) with numerical methods, focusing on an optimized two-stage hybrid block method for solving complex partial differential equations (PDEs). The method combines ANNs with traditional solvers to improve computational efficiency and accuracy, using a Radial Basis Function Neural Network (RBFNN) for optimization. This approach enhances stability, convergence, and adaptability, especially in multidimensional problems, and reduces computational costs while maintaining precision in fields like fluid dynamics and electromagnetism. Simulations show the method outperforms conventional solvers, enabling more efficient real-time simulations in engineering and mathematics.

In this article, we provide effective numerical solutions with high accuracy and exponential convergence for Riesz distributed fractional differential equations. In this paper, in order to solve numerically initial–boundary value problems of RDFDEs in one and two dimensional, we propose and explore a novel collocation approach in two successive steps. The first stage handles the spatial discretization (one and two dimensional spaces), and primarily relies on the shifted Legendre Gauss–Lobatto collocation method. The spatial derivatives that show up in the RDFDEs and the approximate solution are evaluated using an expansion of shifted Legendre polynomials. After that, we reduce the equation and associated conditions to a system of fractional differential equations (SFDEs) for these coefficients. The second step is to propose a Romanovski Gauss–Radau collocation approach for temporal discretization, to reduce such system into a system of algebraic equations which is far easier to be solved. We effectively solved one and two-dimensional RDFDEs using the suggested collocation strategy in both spatial and temporal discretizations, and provided examples to numerically verify the spectral effectiveness and accuracy of the suggested algorithm.

This paper presents an algorithm composed of a class of hybrid block methods blended with a class of neural network optimisation algorithms. The neural network was introduced to enhance the accuracy and stability of numerical hybrid solutions. The hybrid framework synergises the precision of advanced block numerical methods with the function approximation and generalisation capabilities of a radial basis function neural network (RBFNN). By leveraging the strengths of both approaches, the proposed method yields solutions that are computationally efficient and robust. The numerical results obtained from block methods serve as inputs. At the same time, the exact solutions are used as targets to train the RBFNN, enabling the network to refine the solution and effectively handle complex boundary conditions and singularities. This extension significantly improves upon the limitations of existing approaches, particularly in dealing with singular behaviours and achieving superior accuracy. The proposed method is applied to solve a range of challenging partial differential equations, demonstrating its robustness and effectiveness. Comparative analysis highlights its advantages over traditional numerical methods and standalone neural network approaches in terms of accuracy, convergence, and computational efficiency. This hybrid framework establishes a promising direction for integrating numerical methods and machine learning to solve complex mathematical and engineering problems.