Abstract: The matrix description and application of upper and lower approximation of rough set have studied in this paper. The new matrix descriptions of upper and lower approximation under equivalence relations, general binary and covering rough set based on the neighborhood are given. As an application, the inverse problems of upper and lower approximation have solved by using relationship matrix equation, that is, the method to solve[X]is given if the relationship matrix[MR]and the upper approximation[R(X)]（or lower approximation[R(X)]） have known.

Key words: rough set, upper and lower approximation, matrix description, relationship matrix equation

摘要： 主要对粗糙集中上下近似的矩阵刻画及应用进行了研究。给出等价关系、一般二元关系、基于邻域的覆盖粗糙集下一种上下近似的新的矩阵刻画;作为应用，提出关系矩阵方程，并对上下近似的逆问题进行了研究，即在已知关系矩阵[MR,]上（下）近似[R(X)][(R(X))]的情况下反解[X,]给出了求解[X]的方法。

关键词: 粗糙集, 上下近似, 矩阵刻画, 关系矩阵方程