In generalized rough set covering reduction theory,it is necessary to find a new measure to knowledge and rough set because the upper and lower approximations of rough sets are determined by their covering reduction.In this paper,information entropy is introduced to discuss the rough entropy of knowledge and the roughness of rough set,based on generalized rough set covering reduction.A new kind of measurement about the roughness of knowledge and rough set is presented.The conclusion that the rough entropy of knowledge and rough set decreases monotonously as the generalized rough set covering reduction becomes finer is obtained.This paper presents some useful exploration about the incomplete information system from information views.