Graded rough set model based on two universes and its properties

In recent years, much attention has been given to the rough set models based on two universes of discourse and different kinds of rough set models on two universes have been developed from different points of view. In this paper, a novel model, i.e., the graded rough set model on two distinct but related universes (GRSTU) is proposed from the absolute quantitative point of view. We study the basic properties of approximation operators in GRSTU, and introduce a relation matrix based algorithm to compute the lower and upper approximations of a set of objects in GRSTU. Furthermore, the relationships between classical rough set model and GRSTU are discussed and some conclusions related to the GRSTU are given. Finally, several examples are employed to demonstrate the conceptual arguments of GRSTU, and an application of GRSTU is also illuminated in details.