Dependence space of topology and its application to attribute reduction

Attribute reduction plays an important role in pattern recognition and machine learning. Covering-based rough sets, as a technique of granular computing, can be a useful tool for studying attribute reduction. Topology has a close relationship with rough sets and plays a significant role in attribute reduction in information systems. So it is meaningful to combine topology with rough sets to address the problems of attribute reduction. In this paper, we mainly discuss and address the problem of attribute reduction in incomplete information systems with dependence space induced by topological base. Firstly, we investigate the topological structure induced by covering-based rough sets and some characteristics of the topological structure are presented. Secondly, a new type of dependence space is constructed in terms of the base of topological structure, and some characteristics of the dependence space are investigated. Finally, we apply the obtained results of the space to the attribute reduction in incomplete information systems. Especially, a discernibility matrix is defined for the attribute reduction in incomplete information systems.