粗糙近似空间的代数性质

Algebraic properties of rough approximation space

讨论粗糙近似空间的代数性质,证明了一个粗糙近似空间是一个完全分配格即分子格,也是一个正则双Stone代数且为Lukasicwicz三值代数.研究粗糙近似空间中原子的形式,举出反例说明粗糙近似空间不必为原子的,并给出粗糙近似空间是原子的一个充要条件.

The author discusses algebraic properties of rough approximation spaces.It is proved that a rough approximation space is a complete distributive lattice,or a molecular lattice.Furthermore,it is obtained that a rough approximation space is both a regular double-Stone algebra and a Lukasicwicz trivalent algebra.Forms of atoms in a rough approximation space are given and a counter-example shows that a rough approximation space is not necessarily atomic.A necessary and sufficient condition for a rough approximation space to be atomic is obtained.