集族等价与基于粒的下近似算子研究

基于覆盖的粗集是推广经典粗集理论的方法之一，有基于元素、基于粒和基于子系统的3类定义上下近似的途径，以往大多数的文献往往从基于元素的角度出发进行定义。为了研究基于粒的近似算子特别是下近似算子的性质，借鉴格论中既约元、可约元等概念，提出了集族约简的概念。从集族约简出发，探讨了集族等价的概念与性质，并设计了集族约简的算法，得到了两个集族等价是两个集族生成相同的下近似运算的充要条件这一结果，为进一步开展一般二元关系下基于粒的近似算子的公理化方法的研究做了初步的理论方面的准备工作。
Covering based rough set is one of the methods to extend the classical rough set theory. There are three kinds of approaches, the element based definition, the granule based definition, and the subsystem based definition, to define upper and lower approximation. Most of the literature in the past tends to define based on element. In order to study the properties of the granule based approximation operators, especially the lower approximation operator, referring the concepts of irreducible element and reducible element from lattice theory, the concept of collections reduct is put forward. Starting from the concept of collections reduct, the concept and properties of collections equivalence are discussed, and collections reduction algorithm is designed. The result that collections equivalence is the necessary and sufficient condition for generating the same lower approximation by collections is given here. The preliminary theoretical preparation is done here to further develop the axiomatization of the granule based approximation operators under general binary relation