New Kinds of Covering Rough Sets Based on Neighborhood Systems

Abstract

In a covering approximation space, for one object, the intersection of all blocks containing this object is called the neighborhood of the object. Some generalize covering rough sets based on the neighborhood of objects have been studied. For an object, except for the neighborhood of this object, there may exist neighborhoods of other objects containing this object, and we call the collection of all neighborhoods containing this object as neighborhood system of the object. In this paper, we define two types of covering rough sets based on the neighborhood system of the object. Firstly, we investigate the relationship between these covering rough sets based on the neighborhoods and neighborhood systems. Secondly, we study the properties of lower and upper approximations of the new defined covering rough set. Finally, we make a detailed comparison for properties of the lower and upper approximations defined by the neighborhoods and neighborhood systems.