Abstract: This paper mainly discusses the problem about calculating the upper and lower approximates of rough set in approximation space. Because a relation can be represented by a matrix and matrix operations are simple and intuitive, this paper proposes the calculation of the upper and lower approximates in rough set based on relation matrix and matrix operations. Firstly, this paper studies the compositions of two generalized approximation spaces and two generalized fuzzy approximation spaces, discusses the relationships between the operators in the composite approximation space and the two original approximation spaces, and shows that the generalized fuzzy approximation space is the further promotion of the generalized approximation space. Then, according to the matrix representation and the operation of the relation, this paper describes some operations and related properties in approximation space by matrix. Finally, this paper introduces the calculation of the upper and lower approximations of rough set in approximation space in matrix method. The theoretical proof shows that the matrix method is feasible and effective.

Key words: approximation space, composition, rough set, fuzzy set, matrix

摘要： 针对近似空间中粗糙集上、下近似的求解问题，根据关系的矩阵表示和矩阵运算具有简便直观的特点，提出了利用矩阵方法对近似空间中粗糙集上、下近似进行计算。通过研究广义近似空间的复合和广义模糊近似空间的复合问题，首先对复合近似空间的算子和原来近似空间中的算子之间的关系作进一步的探讨，并说明了广义模糊近似空间的复合是广义近似空间复合的进一步推广；进而根据关系的矩阵表示和矩阵运算对近似空间中的一些运算以及相应的性质用矩阵进行了表示；最后对近似空间中粗糙集上、下近似的求解问题，也用矩阵方法进行了计算，理论证明结果显示了该方法是可行有效的。

关键词: 近似空间, 复合, 粗糙集, 模糊集, 矩阵