Apreutesei [1] developed the concept of norm given with the help of the Hausdorff distance from a set to in the almost linear space. This space consists of sets that do not hold the inverse element property with respect to the Minkowski sum. In this paper, we first prove that the rough Hausdorff convergence of a sequence of sets to the set requires the rough convergence of the sequence of norms. Then we give the necessary and sufficient conditions for the rough convergence of the sequence to 0.