Yet Another Kind of Rough Sets Induced by Coverings

A new model of rough sets induced by coverings is proposed. In this new model, the elementary sets are defined as set components generated by a given covering of universe. The new model is compared with two other existing models of rough sets induced by covering and with a standard rough sets where elementary sets are defined by a given equivalence relation. The concept of optimal approximation is also introduced and analyzed for all models discussed in the paper. It is shown that, for a given covering of a universe, our model provides better approximations than the other ones.