Abstract: The generalization of Pawlak’s rough approximation operators is an important issue in rough set theory. This paper presents a new approach for the study of rough approximations on a complete completely distributive lattice (CD lattice). Based on the concept of uncertainty mappings, the paper constructs three pairs of upper and lower rough approximations, discusses their basic properties, and investigates the relationships among these rough approximations. It is pointed out that some well known approximation operators are special cases of the operators presented in this paper.

Key words:  rough set, complete completely distributive lattice (CD lattice), cover, uncertainty mapping, approximation operator

摘要： Pawlak近似算子具有多种推广形式。讨论了完全分配格上的近似算子。通过近似空间中的不确定性映射，分别引入了三种形式的上近似算子及下近似算子，讨论了它们的基本性质及其与已有近似算子之间的关系。研究结果表明，目前文献中出现的多种近似算子可以作为完全分配格上近似算子的特例。

关键词: 粗糙集, 完全分配格, 覆盖, 不确定性映射, 近似算子