Attribute Reduction for Heterogeneous Data Based on the Combination of Classical and Fuzzy Rough Set Models

Attribute reduction with rough sets aims to delete superfluous condition attributes from a decision system by considering the inconsistency between condition attributes and the decision labels. However, heterogeneous condition attributes including symbolic and real-valued ones always coexist for most decision systems and different types of attributes induce different kinds of granular structures. The existing rough set models do not have explicit mechanisms to address different kinds of granular structures reasonably and effectively. In this paper, we aim to perform attribute reduction for decision systems with symbolic and real-valued condition attributes by composing classical rough set and fuzzy rough set models. We first define a discernibility relation for every symbolic and real-valued condition attribute to characterize its discernible ability related to the decision labels. With these discernibility relations, we can develop a dependence function to measure the inconsistency between heterogeneous condition attributes and decision labels, and attribute reduction aims to keep this dependence function with a small perturbation. The proposed attribute reduction deals with heterogeneous condition attributes from the viewpoint of discernible ability and can consider the mutual effects between two types of attributes without preprocessing into single-typed ones. An algorithm to find reducts is developed and experiments are performed to demonstrate that the proposed idea is effective.