Multigranulation rough set model (MGRS) uses multiple equivalence relations on the universe to calculate the approximations, which can solve problem in mutigranulation spaces. In practical applications, information systems often dynamically update due to the variation of objects, attributes or attribute values. Incremental approach is an effective method to calculate approximations for dynamically updated information system. However, existing incremental updating approximations in MGRS mainly focus on single-dimensional variation of objects, attributes or attribute values respectively, without considering multi-dimensional variation of objects, attributes and attribute values. In this paper, we propose matrix-based incremental updating approximations in multigranulation rough set under two-dimensional variation of objects, attributes and attribute values. One is the simultaneous variation of objects and attributes (VOA). The other is the simultaneous variation of objects and attribute values (VOV). First, we give the incremental approaches to update the relevant matrices for the dynamically updated information system due to VOA and VOV. Second, based on the updated matrices, we propose two matrix-based incremental algorithms to update approximations. Finally, examples and experimental results demonstrate the effectiveness of the proposed algorithms for incremental updating approximations in multigranulation rough set under two-dimensional variation.

多粒度粗糙集模型（MGRS）使用宇宙上的多个等价关系来计算近似值，从而可以解决多粒度空间中的问题。在实际应用中，信息系统经常由于对象，属性或属性值的变化而动态更新。增量方法是一种为动态更新的信息系统计算近似值的有效方法。但是，MGRS中现有的增量更新近似主要分别关注对象，属性或属性值的一维变化，而不考虑对象，属性和属性值的多维变化。在本文中，我们提出了在对象二维变化下，多粒度粗糙集中基于矩阵的增量更新近似，属性和属性值。一种是对象和属性的同时变化（VOA）。另一个是对象和属性值（VOV）的同时变化。首先，由于VOA和VOV，我们提供了增量方法来更新动态更新的信息系统的相关矩阵。其次，基于更新的矩阵，我们提出了两种基于矩阵的增量算法来更新近似值。最后，算例和实验结果证明了所提出算法在二维变化下多粒度粗糙集中增量更新近似算法的有效性。由于VOA和VOV，我们提供了增量方法来更新动态更新的信息系统的相关矩阵。其次，基于更新的矩阵，我们提出了两种基于矩阵的增量算法来更新近似值。最后，算例和实验结果证明了所提出算法在二维变化下多粒度粗糙集中增量更新近似算法的有效性。由于VOA和VOV，我们提供了增量方法来更新动态更新的信息系统的相关矩阵。其次，基于更新的矩阵，我们提出了两种基于矩阵的增量算法来更新近似值。最后，算例和实验结果证明了所提出算法在二维变化下多粒度粗糙集中增量更新近似算法的有效性。