Hierarchical Reduction Algorithm of Rough Sets

From the point of view of practical application, a hierarchical reduction algorithm of rough sets theory is proposed. According to the acquisition mode, cost and the real time requirement, the attributes are classified to different parts allocated at several layers in this algorithm. So the knowledge can be presented hierarchically with multiple granularities at multiple layers. And the reduction can hierarchically be applied to part of attributes allocated at each layer instead of all attributes at only one layer. The hierarchical reduct, derived by hierarchical reduction, can solve problem with coarser granularity at lower layer, avoiding solving problem with finer granularity at deeper layer, where the incompleteness maybe exists. The application of this algorithm to complete and incomplete system are discussed. At the same time examples are given, showing the validity and practicability of this algorithm. Furthermore, the information theory basis of this algorithm is put forward and some propositions are proved. Based on these, the relation between information entropy, knowledge granularity and layer is revealed, which help to grip the essence of the algorithm