Abstract As a classical attribute reduction method, granular ball neighborhood rough set(GBNRS) is constrained by the strict requirement that the purity of granular balls must be exactly 1. As a result, a large number of granular balls with a sample size of 1 are generated at the class boundaries. These granular balls are often misjudged as outliers and eliminated, and the loss of boundary information is caused. To address this issue, a fuzzy purity function is first defined. The function integrates membership degree and class labels as an evaluation metric for the quality of granular balls. Based on dynamic quality assessment and optimization strategies, the function takes into account three aspects: the membership degree of data points, the class labels of data points, and the class labels of granular balls. Nextly, during the granular ball splitting process, a classification significance threshold β is introduced, the m value of M-means is adaptively adjusted, and a granular ball generation method based on fuzzy purity is constructed. Furthermore, for the attribute reduction problem in rough set theory, a forward attribute reduction algorithm is designed, and a rough set model based on fuzzy purity granular ball(FPGBRS) is established. Finally, experiments on 12 real datasets demonstrate that FPGBRS can improve classification accuracy and efficiency.
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