序半群中的粗糙集

Rough Sets in Ordered Semigroups

介绍了序半群中粗糙集的概念,这个概念是一般半群中子集的拓广. 对给定的一个子集,给出了一个序半群的正则同余的关于该子集上下近似的定义,讨论了一些子集的运算和上下近似算子之间的关系,特别是当该子集是理想(左、右理想)时,他们的上下近似也是理想.

In this paper, the notion of a rough set in an ordered semigroup is introduce is introduced, which is an extended notion of a subset of an ordered semigroup. For a subset of an ordered semigroup, the notion of upper ( lower) approximation about a regular congruence on an ordered semigroup is introduced. The relationships between operations of subsets of an ordered semigroup and the upper (lower) operators are discussed. Especially, the upper (lower) approximations of ideals (left, right ideals) of an ordered semigroup are ideals (left, right ideals).