  In this paper, we have studied first the idea of rough continuity of real
valued functions of real variables and then we have discussed some important
properties of rough continuity. Then we study the idea of rough $I$-continuity
of real valued functions and find the relation between rough $I$-continuity and
rough continuity. We also introduce the notion of rough $(I_1, I_2)$-continuity
and rough $I^*$-continuity of real valued functions and discuss some properties
on this two types on continuity.
