Knowledge approximations and representations in binary granular computing

The primary goal of this paper is to develop knowledge approximations and representations on binary relation from the view of granular computing (GrC). In rough sets (RS), approximations can be defined by two equivalent views, topology and elementary knowledge. The latter view does not behave well mathematically, so in GrC, topology has often been adopted. Unfortunately, such approximations, called closure and interior, can not be interpreted elementary knowledge. In this paper, we show that they can be interpreted by central knowledge. and based on which knowledge representation is developed. Many examples are used to illustrate the idea.