Parameterized reduction of covering decision systems

Covering rough sets, which generalize classical rough sets only in discrete data sets, deal with set-valued data sets for the decision system. In this paper, we develop the concept of confidence and θ-reduction with covering rough sets which can be used to study inconsistent decision system. However, inconsistent decision systems´ reduction aims to consider all possible rules into possibility and deal with noise and inconsistency. For set-valued data sets, θ-reduction with covering rough sets mainly delete superfluous attributes and keep the possible rules´ confidence not lower than the prescribed threshold. In the study of θ-reduction with covering rough sets, the minimal elements are sufficient to find θ-reduction in the discernibility matrix. An example demonstrates that algorithms can greatly get 6-reduction based on covering rough sets.