粗糙集的近似集

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,它通过两个精确的上、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X(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.%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 upper-approximation 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 A" (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 granularity 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.