覆盖粗糙集上下近似的对偶性分析

摘要

覆盖粗糙集是经典粗糙集的推广.然而,覆盖粗糙集的上下近似定义的方法有很多,上下近似是否对偶一直是争论的焦点.本文分析覆盖粗糙集上下近似的对偶性质,讨论对偶下的正域、负域及边界的可定义性.通过对偶性质的分析,对不同问题使用不同上下近似的方法.进一步研究约简与对偶运算的关系,分析覆盖粗糙集中满足对偶的两对重要的上下近似.%Covering-based rough set theory is an extension of the classical rough set theory. In a variety of definitions of approximations operations, duality is always the focus of debate. This paper analyses duality of approximation operations through the definable properties of positive region, negative region and boundary region. With duality, this paper shows how to choose approximation operations for different applications. This paper also investigates the duality of approximation operations in reduct covering. Finally, the paper analyzes two pairs of approximation operations satisfying the duality in covering-based rough sets.