Approximation Sets of Rough Sets

DOI：10.3724/SP.J.1001.2012.04226

 作者 单位 E-mail 张清华 重庆邮电大学 系统理论及其应用研究中心,重庆 400065计算智能重庆市重点实验室(重庆邮电大学),重庆 400065 zhangqh@cqupt.edu.cn 王国胤 计算智能重庆市重点实验室(重庆邮电大学),重庆 400065 肖雨 计算智能重庆市重点实验室(重庆邮电大学),重庆 400065

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 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.
HTML  下载PDF全文  查看/发表评论  下载PDF阅读器