Abstract: In rough sets based on two different universes, both in theory and applications, matrix methods are all simple and effective calculation methods. This paper studies some matrix properties of rough sets based on two different universes. The relation matrix based on two different universes is proposed, and two square matrices through the relation matrix and its transpose are constructed. The two square matrices are used to investigate some properties of rough sets based on two different universes. A new operation between Boolean matrices is defined. Through this new operation, the upper approximation operator of the covering-based rough sets and the lower operator of the relation-based rough sets based on two different universes are both represented.

Key words: rough set, two different universes, approximation operator, matrix

摘要： 在双论域粗糙集中，不论是理论上还是应用上，矩阵方法都是一种简单且高效的计算方法。利用矩阵的方法来研究双论域粗糙集。提出了双论域上的关系矩阵，通过关系矩阵以及关系矩阵的转置，构造了两个布尔方阵。利用这两个布尔方阵的特征研究了双论域覆盖粗糙集的一些性质。定义了一种布尔矩阵之间新的运算，并且利用这个运算，简洁地表示了双论域覆盖粗糙集的上近似算子和关系粗糙集的下近似算子。

关键词: 粗糙集, 双论域, 近似算子, 矩阵