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Rough sets, especially fuzzy rough sets, are supposedly a powerful mathematical tool to deal with uncertainty in data analysis. This theory has been applied to feature selection, dimensionality reduction, and rule learning. However, it is pointed out that the classical model of fuzzy rough sets is sensitive to noisy information, which is considered as a main source of uncertainty in applications. This disadvantage limits the applicability of fuzzy rough sets. In this paper, we reveal why the classical fuzzy rough set model is sensitive to noise and how noisy samples impose influence on fuzzy rough computation. Based on this discussion, we study the properties of some current fuzzy rough models in dealing with noisy data and introduce several new robust models. The properties of the proposed models are also discussed. Finally, a robust classification algorithm is designed based on fuzzy lower approximations. Some numerical experiments are given to illustrate the effectiveness of the models. The classifiers that are developed with the proposed models achieve good generalization performance.