Rough set theory is one of the most widely used and significant approaches for handling incomplete information. It divides the universe in the beginning and uses equivalency relations to produce blocks. Numerous generalized rough set models have been put out and investigated in an effort to increase flexibility and extend the range of possible uses. We introduce four new generalized rough set models that draw inspiration from "neighborhoods and primals" in order to make a contribution to this topic. By minimizing the uncertainty regions, these models are intended to assist decision makers in more effectively analyzing and evaluating the provided data. We verify this goal by demonstrating that the existing models outperform certain current method approaches in terms of improving the approximation operators (upper and lower) and accuracy measurements. We claim that the current models can preserve nearly all significant aspects associated with the rough set model. Preserving the monotonic property, which enables us to assess data uncertainty and boost confidence in outcomes, is one of the intriguing characterizations derived from the existing models. With the aid of specific instances, we also compare the areas of the current approach. Finally, we demonstrate that the new strategy we define for our everyday health-related problem yields more accurate findings.

A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimension. We show that it outperforms multilayer perceptrons in terms of accuracy and converges faster. We also compare it with several proposed KAN networks: the original spline-based KAN network appears to be more effective for smooth functions, while the P1-KAN network is more effective for irregular functions.

The precise and large dataset concerning catastrophic events is very important for insurers. To improve the quality of such data three methods based on the bootstrap, bootknife, and GAN algorithms are proposed. Using numerical experiments and real-life data, simulated outputs for these approaches are compared based on the mean squared (MSE) and mean absolute errors (MAE). Then, a direct algorithm to construct a fuzzy expert's opinion concerning such outputs is also considered.

Statistical inference tasks, such as constructing confidence regions or simultaneous confidence intervals, are often addressed by deriving distributional theory such as central limit theorems (CLTs) for the estimator in use. Due to the high dimensionality of modern science and engineering applications, there has been a surge of interests in deriving convergence results that are valid in a finite-sample manner. In Reinforcement Learning (RL), a discipline that underpins many recent machine learning breakthroughs (Agarwal et al. (2019); Sutton and Barto (2018)) one central question is to evaluate with confidence the quality of a given policy, measured by its value function. As RL is often modeled as decision making in Markov decision processes (MDPs), the task of statistical inference needs to accommodate the online nature of the sampling mechanism. Temporal Difference (TD) learning (Sutton (1988)) is arguably the most widely used algorithm designed for this purpose. TD learning, which is an instance of stochastic approximation (SA) method (Robbins and Monro (1951)), approximates the value function of a given policy in an iterative manner. Towards understanding the non-asymptotic convergence rate of TD to the target value function, extensive recent efforts have been made (see, e.g.

Customer churn, particularly in the telecommunications sector, influences both costs and profits. As the explainability of models becomes increasingly important, this study emphasizes not only the explainability of customer churn through machine learning models, but also the importance of identifying multivariate patterns and setting soft bounds for intuitive interpretation. The main objective is to use a machine learning model and fuzzy-set theory with top-\textit{k} HUIM to identify highly associated patterns of customer churn with intuitive identification, referred to as Highly Associated Fuzzy Churn Patterns (HAFCP). Moreover, this method aids in uncovering association rules among multiple features across low, medium, and high distributions. Such discoveries are instrumental in enhancing the explainability of findings. Experiments show that when the top-5 HAFCPs are included in five datasets, a mixture of performance results is observed, with some showing notable improvements. It becomes clear that high importance features enhance explanatory power through their distribution and patterns associated with other features. As a result, the study introduces an innovative approach that improves the explainability and effectiveness of customer churn prediction models.

Linguistic fuzzy information evolution is crucial in understanding information exchange among agents. However, different agent weights may lead to different convergence results in the classic DeGroot model. Similarly, in the Hegselmann-Krause bounded confidence model (HK model), changing the confidence threshold values of agents can lead to differences in the final results. To address these limitations, this paper proposes three new models of linguistic fuzzy information dynamics: the per-round random leader election mechanism-based DeGroot model (PRRLEM-DeGroot), the PRRLEM-based homogeneous HK model (PRRLEM-HOHK), and the PRRLEM-based heterogeneous HK model (PRRLEM-HEHK). In these models, after each round of fuzzy information updates, an agent is randomly selected to act as a temporary leader with more significant influence, with the leadership structure being reset after each update. This strategy increases the information sharing and enhances decision-making by integrating multiple agents' evaluation information, which is also in line with real life (\emph{Leader is not unchanged}). The Monte Carlo method is then employed to simulate the behavior of complex systems through repeated random tests, obtaining confidence intervals for different fuzzy information. Subsequently, an improved golden rule representative value (GRRV) in fuzzy theory is proposed to rank these confidence intervals. Simulation examples and a real-world scenario about space situational awareness validate the effectiveness of the proposed models. Comparative analysis with the other models demonstrate our ability to address the echo chamber and improve the robustness.

Fuzzy Neural Networks (FNNs) are effective machine learning models for classification tasks, commonly based on the Takagi-Sugeno-Kang (TSK) fuzzy system. However, when faced with high-dimensional data, especially with noise, FNNs encounter challenges such as vanishing gradients, excessive fuzzy rules, and limited access to prior knowledge. To address these challenges, we propose a novel fuzzy system, the Self-Constructing Multi-Expert Fuzzy System (SOME-FS). It combines two learning strategies: mixed structure learning and multi-expert advanced learning. The former enables each base classifier to effectively determine its structure without requiring prior knowledge, while the latter tackles the issue of vanishing gradients by enabling each rule to focus on its local region, thereby enhancing the robustness of the fuzzy classifiers. The overall ensemble architecture enhances the stability and prediction performance of the fuzzy system. Our experimental results demonstrate that the proposed SOME-FS is effective in high-dimensional tabular data, especially in dealing with uncertainty. Moreover, our stable rule mining process can identify concise and core rules learned by the SOME-FS.

The rapid evolution of Brain-Computer Interfaces (BCIs) has significantly influenced the domain of human-computer interaction, with Steady-State Visual Evoked Potentials (SSVEP) emerging as a notably robust paradigm. This study explores advanced classification techniques leveraging interpretable fuzzy transfer learning (iFuzzyTL) to enhance the adaptability and performance of SSVEP-based systems. Recent efforts have strengthened to reduce calibration requirements through innovative transfer learning approaches, which refine cross-subject generalizability and minimize calibration through strategic application of domain adaptation and few-shot learning strategies. Pioneering developments in deep learning also offer promising enhancements, facilitating robust domain adaptation and significantly improving system responsiveness and accuracy in SSVEP classification. However, these methods often require complex tuning and extensive data, limiting immediate applicability. iFuzzyTL introduces an adaptive framework that combines fuzzy logic principles with neural network architectures, focusing on efficient knowledge transfer and domain adaptation. iFuzzyTL refines input signal processing and classification in a human-interpretable format by integrating fuzzy inference systems and attention mechanisms. This approach bolsters the model's precision and aligns with real-world operational demands by effectively managing the inherent variability and uncertainty of EEG data. The model's efficacy is demonstrated across three datasets: 12JFPM (89.70% accuracy for 1s with an information transfer rate (ITR) of 149.58), Benchmark (85.81% accuracy for 1s with an ITR of 213.99), and eldBETA (76.50% accuracy for 1s with an ITR of 94.63), achieving state-of-the-art results and setting new benchmarks for SSVEP BCI performance.

Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.

Mosques are worship places of Allah and must be preserved clean, immaculate, provide all the comforts of the worshippers in them. The prophet's mosque in Medina/ Saudi Arabia is one of the most important mosques for Muslims. It occupies second place after the sacred mosque in Mecca/ Saudi Arabia, which is in constant overcrowding by all Muslims to visit the prophet Mohammad's tomb. This paper aims to propose a smart dome model to preserve the fresh air and allow the sunlight to enter the mosque using artificial intelligence techniques. The proposed model controls domes movements based on the weather conditions and the overcrowding rates in the mosque. The data have been collected from two different resources, the first one from the database of Saudi Arabia weather's history, and the other from Shanghai Technology Database. Congested Scene Recognition Network (CSRNet) and Fuzzy techniques have applied using Python programming language to control the domes to be opened and closed for a specific time to renew the air inside the mosque. Also, this model consists of several parts that are connected for controlling the mechanism of opening/closing domes according to weather data and the situation of crowding in the mosque. Finally, the main goal of this paper has been achieved, and the proposed model has worked efficiently and specifies the exact duration time to keep the domes open automatically for a few minutes for each hour head.