中文摘要：

讨论覆盖粗糙集在协调映射下的不变性质，指出满的协调映射可以保证原覆盖近似空间的三类覆盖上近似与像覆盖近似空间覆盖上近似之间一一对应。而且原覆盖近似空间的约简的像为像覆盖近似空间的约简。

英文摘要：

Invariance properties of covering-based rough sets under consistent function are discussed.It is proved that there exist one-to-one correspondences between covering upper approximations of original approximation space and cov-ering upper approximations of image approximation space under consistent function.Furthermore,the image of reduc-tion of original approximation space is the reduction of image approximation space.