Research of reduct features in the variable precision rough set model

Rough set theory is a new mathematic tool aimed at data analysis problems involving uncertain or imprecise information. As an important extended rough set model, variable precision rough set model (VPRSM), which was introduced by Ziarko, enhances the ability to deal with datasets which have noisy data. Reduct is one of the most important notions in rough set application to data mining as well as in VPRSM. Unfortunately, there are some anomalies in the procedure of attribute reduction using Ziarko's reduct definition, therefore, defining and finding more reasonable reducts are in requirements. Some kinds of reduction anomalies are analyzed in detail, the concept of inclusion degree (beta) threshold is put forward and the relationship between inclusion degree and classification quality is discussed in this paper. The reduct definition extends from a specific beta value to a beta interval, and reduct hierarchy was constructed based on beta interval features. Then reduct can be elucidated from different levels (viz., the quality of classification, positive region and decision class), and reduction anomalies can be eliminated gradually according to restricting reduct definition conditions. All of these notions develop the variable precision rough set mode further. (C) 2008 Elsevier B.V. All rights reserved.