Minimal attribute reduction with rough set based on compactness discernibility information tree

Minimal attribute reduction plays an important role in rough set. Heuristic algorithms are proposed in literature reviews to get a minimal reduction and yet an unresolved issue is that many redundancy non-empty elements involving duplicates and supersets exist in discernibility matrix. To be able to eliminate the related redundancy and pointless elements, in this paper, we propose a compactness discernibility information tree (CDI-tree). The CDI-tree has the ability to map non-empty elements into one path and allow numerous non-empty elements share the same prefix, which is recognized as a compact structure to store non-empty elements in discernibility matrix. A complete algorithm is presented to address Pawlak reduction based on CDI-tree. The experiment results reveal that the proposed algorithm is more efficient than the benchmark algorithms to find out a minimal attribute reduction.