Study On Hierarchical Reduction Approaches In Rough Sets Theory

In this paper, according to the recognition laws of human being, a series of RST (Rough Sets Theory) hierarchical reduction approaches, which are important to data mining and information fusion, are proposed and studied.Firstly, a hierarchical reduction approach of RST is proposed. In this approach, according to the acquisition mode, cost and the real time requirement, the attributes are classified to different parts allocated at several layers. So the knowledge in the information system 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. This approach is very applicable to practice.Based on the information theory, it is proved that the entropy of information system and the mutual information of decision system are constant in the hierarchization of attributes. So the RST hierarchical reduction approaches have strict mathematic basis. The application in acquiring the control decision of a cement kiln shows the validity of the hierarchical reduction approach.Secondly, two extended RST hierarchical reduction approaches are proposed to accomplish two important process of RST-completion and discretization, respectively. In addition, an extended approach is imported.Extended approach one: the hierarchical reduction approach of RST to incomplete information system. This approach represents knowledge with complete and incomplete attributes layers, and then conduct reduction hierarchically at each layer. It is proved that this approach reduces the entropy of information system and the mutual information of decision system. According to information theory, this approach is better than other completion methods, such as Remove incompletes, Mean/mode fill, Combinatorial completion and Similarity relation model. Moreover, the application of hierarchical reducts can avoid the reasons for incompletion, such as the hard acquisition mode, high cost and the high real time requirement.Extended approach two: this approach based on the combination of rough sets theory and BP neural network. It processes the discrete and continue attributes with rough sets and BP neural network respectively, which can avoid the uncertainty caused by the discretization of the continue attributes. At the same time, rough sets is high sensitivity to the noise in the decisionsystem, which can be counterbalance by BP neural network.Extended approach three: a hierarchical reduction approach is imported, which is based on the combination of statistical feature selection and linear discriminant analysis. This hierarchical reduction approach extends the simple classified attributes reduction to attributes selection and attributes reduction.Furthermore, the properties and the case study of these three extended approaches are expatiated respectively.Finally, some new ideas are proposed to construct extended hierarchical reduction approaches, including related hierarchical reduction approaches and the hierarchical reduction approaches integrated with other artificial intelligent approaches to solve specific problems.