Weighted rough set learning: Towards a subjective approach

Classical rough set theory has shown powerful capability in attribute dependence analysis, knowledge reduction and decision rule extraction. However, in some applications where the subjective and apriori knowledge must be considered, such as cost-sensitive learning and class imbalance learning, classical rough set can not obtain the satisfying results due to the absence of a mechanism of considering the subjective knowledge. This paper discusses problems connected with introducing the subjective knowledge into rough set learning and proposes a weighted rough set learning approach. In this method, weights are employed to represent the subjective knowledge and a weighted information system is defined firstly. Secondly, attribute dependence analysis under the subjective knowledge is performed and weighted approximate quality is given. Finally, weighted attribute reduction algorithm and weighted rule extraction algorithm are designed. In order to validate the proposed approach, experimentations of class imbalance learning and cost-sensitive learning are constructed. The results show that the introduction of appropriate weights can evidently improve the performance of rough set learning, especially, increasing the accuracy of the minority class and the AUC for class imbalance learning and decreasing the classification cost for cost-sensitive learning.