覆盖粗糙集上下近似的分类

Classification of lower and upper approximations on covering rough sets

覆盖粗糙集是经典粗糙集理论的推广。对于其上下近似,从不同角度可以得到不同的定义。文中分析覆盖粗糙集不同上近似间的区别与联系,总结定义覆盖粗糙集上近似的方法。对样点进行详细地分类,提出强正点、弱正点,弱正边点、正边点以及对应的强负点、弱负点、弱负边点、负边点等概念。利用这些概念对覆盖粗糙集的上下近似进行分类,对各类上下近似的对偶性、正域负域及边界的可定义进行对比。通过上下近似的分类对比,可以定义出更多满足应用需要的上下近似。

Covering rough set theory is an extension of the traditional rough set theory. Researchers proposed different definition sets of upper/lower approximations from different viewpoints. This paper proposes the concept of point-covering, under which those definition sets can be more clearly distinguished. Specifically, it proposes a number of concepts including strong-positive-point, weak- positive-point, weak-positive-border-point and corresponding strong-negative-point, weak-negative-point, and weak-negative-border-point. Those concepts are employed to classify different definition sets of upper/lower approximations. Duality and other properties of those definition sets are also discussed. Based on this work, more upper/lower approximation definition sets can be developed to suit the requirement of applications.