Extended rough sets model based on fuzzy granular ball and its attribute reduction

Attribute reduction is one of the core steps of data analysis. The attribute reduction method based on neighborhood rough sets (NRS) is widely used. However, the time complexity of this method is excessively high because its radius selection relies on grid search. Granular ball neighborhood rough sets (GBNRS) can generate different neighborhoods adaptively and has more generality and flexibility than the NRS method. Nevertheless, due to the purity of granular ball is required to be 1, the GBNRS algorithm will generate many granular balls with the sample number of 1 at the boundaries of classes. These granular balls will be regarded as outliers and deleted, resulting in the loss of class boundary information. Moreover, due to the strict reduction conditions of GBNRS, the reduction effect cannot be achieved on some datasets. To solve the above problems, the fuzzy granular ball is defined by relaxing the generation conditions of the granular ball, and an extended rough sets model is proposed on the basis of the fuzzy granular ball (FGBERS). In this model, we retain as much class boundary information as possible by preserving the fuzzy granular ball of class boundary. A new forward heuristic attribute reduction algorithm is designed on the basis of this model. To demonstrate the performance of FGBERS, we conducted sufficient experiments on 18 real datasets from different fields. The experimental results show that FGBERS not only compensates for the shortcomings of GBNRS, but also demonstrates higher classification accuracy, especially on the KNN classifier, the classification accuracy of the FGBERS algorithm is 5% higher on average, and the highest improvement is 20% on high-dimensional dataset ALLAML. In addition, compared with the comparison algorithms, FGBERS has excellent reduction performance in both large-scale datasets and high-dimensional datasets.