Fuzzy rough set theory is sensitive to noisy samples as the fuzzy approximations are proposed based on sensitive statistics, i.e. minimum and maximum. Here, we develop a robust fuzzy rough set model called probability granular distance-based fuzzy rough sets (PGDFRS), in which the similarity between samples is substituted by that between granules to reduce the impact of noise on the statistical minimum and maximum. The robust principle is to take the probability density values of samples as weights for computing probability distances between granules. By using PGDFRS, a feature selection algorithm is created. This algorithm limits feature selection to two-dimensional space and avoids the difficulty of parameter setting in high-dimensional space. The experimental results indicate that the designed feature selection algorithm is effective and robust. Additionally, it confirms that the proposed PGDFRS model is more robust than some existing fuzzy rough set models.

由于基于敏感统计量（即最小值和最大值）提出了模糊近似，因此模糊粗糙集理论对噪声样本敏感。在这里，我们开发了一种鲁棒的模糊粗糙集模型，称为概率概率基于距离的模糊粗糙集（PGDFRS），其中样本之间的相似性被颗粒之间的相似性替代，以减少噪声对统计最小值和最大值的影响。鲁棒性原则是将样本的概率密度值作为权重，以计算颗粒之间的概率距离。通过使用PGDFRS，可以创建特征选择算法。该算法将特征选择限制在二维空间，避免了在高维空间进行参数设置的困难。实验结果表明，所设计的特征选择算法是有效且鲁棒的。