Data volume reduction in covering approximation spaces with respect to twenty-two types of covering based rough sets

•Studying consistent mappings as homomorphisms for 22 pairs of covering approximation operators.•Studying whether consistent mappings preserve the definability of sets with respect to these 22 pairs.•Introducing the measure of consistency of a covering and investigating its role in the compressing a covering space.•Proposing algorithms to compress covering approximations and reducing volume of the underlying data by consistent mappings.•Applying the proposed algorithms to some real world datasets.

In this paper, we investigate whether consistent mappings can be used as homomorphism mappings between a covering based approximation space and its image with respect to twenty-two pairs of covering upper and lower approximation operators. We also consider the problem of constructing such mappings and minimizing them. In addition, we investigate the problem of reducing the data volume using consistent mappings as well as the maximum amount of their compressibility. We also apply our algorithms against several datasets.