Recent work in the area of Knowledge Representation and Reasoning has focused on modification and optimization of knowledge bases (KB) through the use of forgetting operators of the form forget(KB, (R) over bar), where (R) over bar is a set of relations in the language signature used to specify the KB. The result of this operation is a new KB where the relations in (R) over bar are removed from the KB in a principled manner resulting in a more efficient representation of the KB for different purposes. The forgetting operator is also reflected semantically in terms of the relation between the original models of the KB and the models for the revised KB after forgetting. In this paper, we first develop a rough reasoning framework where our KBs consist of rough formulas with a semantics based on a generalization of Kleene algebras. Using intuitions from the classical case, we then define a forgetting operator that can be applied to rough KBs removing rough relations. A constructive basis for generating a new KB as the result of applying the forgetting operator to a rough KB is specified using second-order quantifier elimination techniques. We show the application of this technique with some practical examples.