Research Of Knowledge Reductions And Approximation Operators In Composite Systems

The rough set theory proposed by Pawlak is an effective mathematical tool to deal with imprecise, incomplete and uncertain data. In recent years, the research on rough sets has been extended to many fields, and a variety of generalized rough set models are established. However, each generalized rough set only can be used to deal with the data that contain one attribute, the data which contain multiple different attributes cannot be processed. We focuse on knowledge reductions and approximation operators for composite ayatems. The main contents are as follows:For the reduction of composite systems. Firstly, based on the minimal description, the reduction of composite information system are proposed from two aspects of local and global respectively, local reduction and global reduction algorithms are designed. Secondly, by intro-ducing the minimal description and maximal description, the inter-class information and intra-class information of composite decision system are considered, the inter-class reduct, intra-class reduct and construct algorithm are proposed respectively. Finally, discernibility matrix-based method to compute all reducts for composite system and composite decision system are pre-sented. Examples show that these algorithms are effective.For the rough approximation of composite information systems, four types of approximation operators are structured based on the minimal description. Their properties are presented, and the relationship between them are analyzed. We proved that the accuracy based on minimal description is more high than the existing accuracy based on compodite relation.