The first type of graded rough set based on rough membership function

The extension of classical rough set model is a very hot and interesting topic. In this paper, our aim is to present the first type of graded rough set (FGRS) based on rough membership function. The concepts of k-regions, k-rough degree, etc., are proposed firstly, and some of important properties are investigated in this rough set model. Moreover, the model has the corresponding properties with classical rough set model. In addition, relative k-reduction is considered and an example is used to illustrate its validity. By comparing, one can find that the model is a generalization of variable precision rough set model.