Measuring roughness of generalized rough sets induced by a covering

In this paper, we propose new lower and upper approximations and obtain some important properties in generalized rough set induced by a covering. Especially, these properties are compared with ones of Pawlak's rough sets and Bonikowski's covering generalized rough sets, respectively. Moreover, we define a measure of roughness based on generalized rough sets with the new approximations and discuss some significant properties of the measure.