From the point of that knowledge can be seen as the ability to perform classifications, a new kind of measurement of rough set, based on general binary relations, was presented. It is found that the α entropy and α accuracy increase monotonously while α roughness decreases monotonously as the information granularities become smaller. By means of the α entropy knowledge, definitions of α accuracy and α roughness were derived, and the α accuracy and α roughness are more reasonable and accurate than those obtained in the classical methods. These results develop the theory of uncertainty and provide theoretical basis for knowledge acquisition in information systems based on general binary relation.