A novel method for attribute reduction of covering decision systems

Attribute reduction has become an important step in pattern recognition and machine learning tasks. Covering rough sets, as a generalization of classical rough sets, have attracted wide attention in both theory and application. This paper provides a novel method for attribute reduction based on covering rough sets. We review the concepts of consistent and inconsistent covering decision systems and their reducts and we develop a judgment theorem and a discernibility matrix for each type of covering decision system. Furthermore, we present some basic structural properties of attribute reduction with covering rough sets. Based on a discernibility matrix, we develop a heuristic algorithm to find a subset of attributes that approximate a minimal reduct. Finally, the experimental results for UCI data sets show that the proposed reduction approach is an effective technique for addressing numerical and categorical data and is more efficient than the method presented in the paper [D.G. Chen, C.Z. Wang, Q.H. Hu, A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets, Information Sciences 177(17) (2007) 3500–3518].