Neighborhood Covering Reduction extracts rules for classification through formulating the covering of data space with neighborhoods. The covering of neighborhoods is constructed based on distance measure and strictly constrained to be homogeneous. However, this strategy over-focuses on individual samples and thus makes the neighborhood covering model sensitive to noise and outliers. To tackle this problem, we construct a flexible Tri-partition Neighborhood for robust classification. This novel neighborhood originates from Three-way Decision theory and is partitioned into the regions of certain neighborhood, neighborhood boundary and non-neighborhood. The neighborhood boundary consists of uncertain neighbors and is helpful to tolerate noise. Besides the neighborhood construction, we also proposed complete and partial strategies to reduce redundant neighborhoods to optimize the neighborhood covering for classification. The reduction process preserves lower and upper approximations of neighborhood covering and thereby provides a flexible way to handle uncertain samples and noise. Experiments verify the classification based on tri-partition neighborhood covering is robust and achieves precise and stable results on noisy data.