Abstract: This paper defines the partial ordering relation of the Boole ring, studies the Boole ring closure operator and interior operator properties. Thus, it introduces the approximation spaces of congruence and congruence upper and lower approximation operator in congruence approximation spaces. At last, the paper studies properties of the upper and lower approximate operators.

Key words: rough set, Boole ring, approximation operator

摘要： 从定义Boole环上的偏序关系入手，研究了Boole环上闭算子和内部算子的性质，由此引入了同余近似空间和同余近似空间中上近似和下近似算子的定义，研究了上近似算子和下近似算子的性质。

关键词: 粗糙集, Boole环, 近似算子