  In this paper, we have introduced first the notion of rough $I^*$-convergence
in a normed linear space as an extension work of rough $I$-convergence and then
rough $I^K$-convergence in more general way. Then we have studied some
properties on these two newly introduced ideas. We also examined the
relationship between rough $I$-convergence with both of rough $I^*$-convergence
and rough $I^K$-convergence.
