A new method of attribute reduction for covering rough sets

As traditional rough sets are mainly used to exact decision rules and reduce attributes from the database, covering rough sets as an important generalization of traditional rough sets does the similar work for more complex database. Attribute reduction is a core problem in covering rough sets. The discernibility matrix is the theoretical foundation of finding attribute reduction. In this paper, we find it is unnecessary to compute all the elements of discernibility matrix, and we need to only find its minimal elements. The minimal element of discernibility matrix is the sufficient condition to compute attribute reductions with covering rough sets, and every minimal element is determined by one sample pair at least. Based on the above work, in this paper, firstly we define the relative discernibility relation. Secondly we develop the algorithm to find the minimal elements of covering rough sets by using the corresponding relationship between the minimal elements and sample pairs. Finally, we give the algorithm of finding a reduct based on covering rough sets by applying the relative discernibility relationship.