Hierarchical reduction approach of rough sets theory and its basis on the information theory
粗糙集理论的分层递阶约简算法及其信息理论基础

Simulating the hierarchical principle of human cognizance process, a hierarchical reduction algorithm of rough set theory is proposed in this paper. In the algorithm, the attributes are firstly partitioned into different parts allocated at several layers. Then the knowledge in the information systems or decision systems is presented hierarchically with multiple granularities at multiple layers, and the reduction is hierarchically applied to parts of attributes allocated at each layer. The algorithm has a strong applicability and a good dynamic property, and it can be implemented in parallel. At the same time, the foundation of the algorithm is justified on the basis of information theory. Finally, the hierarchical reduction algorithm is used to acquire the control decision of a cement kiln, which verifies the effectiveness of the algorithm.