粗糙集中几种粒结构的代数关系

Algebraic Relation of Several Granular Structures in Rough Sets

针对目标概念在近似空间上存在多种粒结构的问题,通过讨论目标概念的最优近似集与Pawlak近似集、变精度近似集之间的代数关系,得到最优近似集与Pawlak下、上近似集、变精度下、上近似集的等价条件;通过分析基于最优近似、基于Pawlak近似、基于变精度近似的分布约简之间的关系,得到在一定条件下,最优近似分布约简为Pawlak近似与变精度近似的分布约简.研究结果表明:根据目标概念与基本知识粒之间不同的近似刻画,不仅可以建立不同的粗糙集模型,还可以建立不同的分布约简.

To the problem of existing many kinds of granular structures on approximation space, the algebraic relations among the optimal approximation set, Pawlak lower and upper approximation set and the variable precision lower and upper approximation set of the target concept are discussed. The equivalent conditions of the optimal approximation set between Pawlak approximation set, the variable precision approximation set are obtained. The relationships among the distribution reduction based on the optimal approximation, the distribution reduction based on the Pawlak approximation and the distribution reduction based on the variable precision approximation are analyzed. Under certain conditions, the conclusions that the optimal approximate distribution reduction is Pawlak approximation and variable precision approximation distribution reduction are presented. It can be seen from these above conclusions that the different rough set models can not only be established, but also different distribution reduction can be established according to the different approximate characterization between the target concept and the basic granular.