中文摘要：

粗糙集是1982年由Pawlak教授提出的解决集合边界不确定的重要方法庀通过两个精确的上、下近似集作为边界线来刻画目标集合（概念）X的不确定性，但它没有给出如何用已知的知识基（知识粒）来精确或近似地描述边界不确定的目标集合（概念）X的方法．首先给出了集合之间的相似度概念，然后分析了分别用上近似集R-（X）和下近似集R-（X）作为目标集合（概念）X近似描述的不足，提出了在已有知识基（粒）空间下寻找目标集合（概念）X的近似集的方法，并分析了用R0.5（X）作为坝概念）的近似集的优越性．最后讨论了不同知识粒度空间下R0.5（X）与X的相似度随知识粒度的变化关系．从新的角度提出了目标集合（概念）X近似集的构造方法，促进了粗糙集模型的发展．

英文摘要：

Rough sets proposed by professor Pawlak in 1982 is an important tool to process the uncertainty of a set＇s boundary, and it describes the uncertainty of set X （or concept） with two crisp boundaries that are upperapproximation set and lower-approximation set of X. However, a rough set does not give out the method for precisely, or approximately describe the uncertain set X （or concept） with existing knowledge base. In this paper, the similaritybetween two sets is proposed at first, the disadvantages of using upper-approximation set R（X） or lower- approximation set R（X） as an approximation set of the uncertain set X （or concept） are analyzed, and then amethod for building an approximation set of the uncertain set X is presented, the conclusion that the set R0.5（X） is the optimal approximation set is proved. Finally, the changing regularities of similarity between R0.5（X） and X with the change of knowledge granulatity in knowledge space are disscussed in detail. From the new viewpoint, this paper presents a new method for building an approximation set of the uncertain set X, and it will promote the development of rough set model.