Abstract: Uncertainty of rough sets has close relatives with the knowledge granularities of the approximation space. A concept of relative knowledge granularities was proposed. The roughness of a rough set based on relative knowledge granularities not only reflects the action of the approximation space, but also gets rid of the effect of the negative region of the rough set. A new kind of fuzziness of rough sets based on boundary entropy was designed. Both of the roughness and fuzziness are monotonously decreasing with the refining of knowledge granularities in approximation spaces.

Key words: Rough sets,Knowledge granularities,Roughness,Fuzziness,Uncertainty