Comparison of six types of rough approximations based on <i>j</i> -neighborhood space and <i>j</i> -adhesion neighborhood space

Abstract

In this paper, we generalize three types of rough set models based on j -neighborhood space (i.e, type 1 j -neighborhood rough set, type 2 j -neighborhood rough set, and type 3 j -neighborhood rough set), and investigate some of their basic properties. Also, we present another three types of rough set models based on j -adhesion neighborhood space (i.e, type 4 j -adhesion neighborhood rough set, type 5 j -adhesion neighborhood rough set, and type 6 j -adhesion neighborhood rough set). The fundamental properties of approximation operators based on j -adhesion neighborhood space are established. The relationship between the properties of these types is explained. Finally, according to j -adhesion neighborhood space, we give a comparison between the Yao’s approach and our approach.