Fuzzy rough set theory is effective for processing datasets with complex attributes, supported by a solid mathematical foundation and closely linked to kernel methods in machine learning. Attribute reduction algorithms and classifiers based on fuzzy rough set theory exhibit promising performance in the analysis of high-dimensional multivariate complex data. However, most existing models operate at the finest granularity, rendering them inefficient and sensitive to noise, especially for high-dimensional big data. Thus, enhancing the robustness of fuzzy rough set models is crucial for effective feature selection. Muiti-garanularty granular-ball computing, a recent development, uses granular-balls of different sizes to adaptively represent and cover the sample space, performing learning based on these granular-balls. This paper proposes integrating multi-granularity granular-ball computing into fuzzy rough set theory, using granular-balls to replace sample points. The coarse-grained characteristics of granular-balls make the model more robust. Additionally, we propose a new method for generating granular-balls, scalable to the entire supervised method based on granular-ball computing. A forward search algorithm is used to select feature sequences by defining the correlation between features and categories through dependence functions. Experiments demonstrate the proposed model's effectiveness and superiority over baseline methods.

Human cognition operates on a "Global-first" cognitive mechanism, prioritizing information processing based on coarse-grained details. This mechanism inherently possesses an adaptive multi-granularity description capacity, resulting in computational traits such as efficiency, robustness, and interpretability. The analysis pattern reliance on the finest granularity and single-granularity makes most existing computational methods less efficient, robust, and interpretable, which is an important reason for the current lack of interpretability in neural networks. Multi-granularity granular-ball computing employs granular-balls of varying sizes to daptively represent and envelop the sample space, facilitating learning based on these granular-balls. Given that the number of coarse-grained "granular-balls" is fewer than sample points, granular-ball computing proves more efficient. Moreover, the inherent coarse-grained nature of granular-balls reduces susceptibility to fine-grained sample disturbances, enhancing robustness. The multi-granularity construct of granular-balls generates topological structures and coarse-grained descriptions, naturally augmenting interpretability. Granular-ball computing has successfully ventured into diverse AI domains, fostering the development of innovative theoretical methods, including granular-ball classifiers, clustering techniques, neural networks, rough sets, and evolutionary computing. This has notably ameliorated the efficiency, noise robustness, and interpretability of traditional methods. Overall, granular-ball computing is a rare and innovative theoretical approach in AI that can adaptively and simultaneously enhance efficiency, robustness, and interpretability. This article delves into the main application landscapes for granular-ball computing, aiming to equip future researchers with references and insights to refine and expand this promising theory.

Most existing fuzzy set methods use points as their input, which is the finest granularity from the perspective of granular computing. Consequently, these methods are neither efficient nor robust to label noise. Therefore, we propose a frame-work called granular-ball fuzzy set by introducing granular-ball computing into fuzzy set. The computational framework is based on the granular-balls input rather than points; therefore, it is more efficient and robust than traditional fuzzy methods, and can be used in various fields of fuzzy data processing according to its extensibility. Furthermore, the framework is extended to the classifier fuzzy support vector machine (FSVM), to derive the granular ball fuzzy SVM (GBFSVM). The experimental results demonstrate the effectiveness and efficiency of GBFSVM.

Naive Bayes has been widely used in many applications because of its simplicity and ability in handling both numerical data and categorical data. However, lack of modeling of correlations between features limits its performance. In addition, noise and outliers in the real-world dataset also greatly degrade the classification performance. In this paper, we propose a feature augmentation method employing a stack auto-encoder to reduce the noise in the data and boost the discriminant power of naive Bayes. The proposed stack auto-encoder consists of two auto-encoders for different purposes. The first encoder shrinks the initial features to derive a compact feature representation in order to remove the noise and redundant information. The second encoder boosts the discriminant power of the features by expanding them into a higher-dimensional space so that different classes of samples could be better separated in the higher-dimensional space. By integrating the proposed feature augmentation method with the regularized naive Bayes, the discrimination power of the model is greatly enhanced. The proposed method is evaluated on a set of machine-learning benchmark datasets. The experimental results show that the proposed method significantly and consistently outperforms the state-of-the-art naive Bayes classifiers.