中文摘要：

将粗糙集的思想引入线性空间，首先对于线性空间V的子空间W，我们定义了一个同余关系ρW，并且给出了同余类的刻画和若干性质。然后定义了线性空间V的非空子集X关于同余ρW的上、下近似，且给出了ρW-上（下）近似的一系列性质。

英文摘要：

In this paper, we introduce the idea of rough sets on linear spaces. For a subspace W of linear space V, we define a congruence relationship ρw in the space linear V and give some characterizations of ρw-congruence class. Moreover we put forward the concepts of upper and lower approximations of a subset in a linear space, and study some properties about upper and lower approximations.