Abstract: Compared to the existing definition of cover’s reduction, reducible element, removable element is redefined and a cover which is more terse than reduced covering is got. Furthermore, the relationship among union-reduced covering, summary covering and minimum description covering is discussed. And it is found that union-reduced covering is the same as summary covering, and summary covering is included in union-reduced covering. At last, the relationship between the operators of summary covering and union-reducible covering is discussed.

Key words: rough set, covering, reduction, summary covering

摘要： 对比现有的覆盖的约简、可约基本集的定义，重新定义了可去基本集和简易覆盖，得到了一个比约简覆盖更简练的简易覆盖。进而，又讨论了简易覆盖与约简覆盖、极小描述覆盖三者之间的关系。得出并-约简覆盖和极小描述覆盖相等，而简易覆盖包含于并-约简覆盖之中，是一个更简练的覆盖这一结论。最后，又讨论了在简易覆盖与并-约简覆盖下，算子之间的关系。

关键词: 粗糙集, 覆盖, 约简, 简易覆盖