Hierarchical reduction approach of rough sets to incomplete systems

This paper proposes a hierarchical reduction approach of rough sets to incomplete information systems. Simulating the recognition laws of a human being, this approach presents knowledge 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 a hierarchical reduction, can solve the problem with coarser granularity at a lower layer, avoiding solving a problem with finer granularity at a deeper layer, where the incompleteness perhaps exists. This approach can make the knowledge reduction simple and fast. Both hierarchical reduction and reduct are applicable to practical problem solving.