粗糙集理论中近似空间的精细及近似精度

Fineness and coarseness of an approximation space in the rough set theory

讨论了近似空间的精细与粗糙的概念及其两个等价描述,研究了给定集合的上下近似集在精细与粗糙近似空间中的性质,即随着近似空间的加细,给定集合X的最佳下近似单调上升、最佳上近似单调下降.还讨论了近似精度问题,指出Pawlak近似精度的一个不合理现象,并且新定义了一种近似精度.

The definition of fineness and coarseness of approximation space and two equivalent descriptions were given. Some behaviors of the best upper （lower）-approximation of sets are examined, the best upper approximation of a given set monotonously declines along with fineness of approximation space, and the best lower approximation of a given set monotonously rises along with fineness of approximation space. The accuracy of approximation was discussed and an unreasonable appearance of Pawlak accuracy was found out.