Novel algorithms of attribute reduction with variable precision rough set model

The variable precision rough set model resists noise in data by introducing a parameter to relax the strict inclusion in approximations of the classical rough set model, and attribute reduction with the variable precision rough set model aims at deleting dispensable condition attributes from a decision system by considering this relaxation. In the variable precision rough set model, the approach of the discernibility matrix is the theoretical foundation of attribute reduction. However, this approach has always heavy computing load, so its effective improvement is clearly of importance in order to find reducts faster. In this paper, we observe that only minimal elements in the discernibility matrix are sufficient to find reducts, and each minimal element is at least determined by one equivalence class pair relative to condition attributes. With this motivation, the relative discernibility relation of a condition attribute is defined to characterize minimal elements in the discernibility matrix, and the algorithm of finding all minimal elements is developed by this characterization. Based on the algorithm of finding all minimal elements, we develop two algorithms to find all reducts and one reduct in variable precision rough sets. Several experiments are performed to demonstrate that our methods proposed in this paper are effective to reduce the computing load.