Dominance-based Rough Set Approach (DRSA) has been proposed to deal with multi-criteria classification problems, where data may be inconsistent with respect to the dominance principle. However, in real-life datasets, in the presence of noise, the notions of lower and upper approximations handling inconsistencies were found to be excessively restrictive which led to the proposal of the variable consistency variant of the theory. In this paper, we deal with a new approach based on DRSA, whose main idea is based on the error corrections. A new definition of the rough set concept known as generalized decision is introduced, the optimized generalized decision. We show its connections with statistical inference and dominance-based rough set theory.