Hierarchical reduction approach of the rough sets theory and its basis on the information theory

From the point of view of practical application, a hierarchical reduction approach of rough sets theory is proposed. In this approach, according to the acquisition mode, cost and real time requirement, the attributes are classified in different parts allocated to several layers. So the knowledge in information systems or decision systems can be presented hierarchically with multiple granularities in multiple layers. The reduction can be applied hierarchically to parts of attributes allocated to each layer. The basis of this approach is proved from information theory. Furthermore, the properties of the approach are discussed, such as practicability, rapidity and dynamic performance. Finally, the hierarchical reduction approach shows its validity in acquiring the control decision of a cement kiln.