The basic morphological gradient, deflned as the difierence of dilation and erosion, has major defect of wide edges. By studying the relationship between rough set theory and mathematical morphology, two morphological gradient operators based on roughness, the stepped approximation and the linear approximation gradient operators are proposed. These two gradient operators describe image border thinner than existing morphological gradients. The stepped approximation gradient operator presents the thinnest boundary lines. The linear approximation gradient operator is described in more informative. From the perspective of rough sets processing uncertain information, such border-domain deflnitions reduce the uncertainty of information and develop the application flelds of rough sets.