An incremental attribute reduction approach based on knowledge granularity for incomplete decision systems

Attribute reduction is a core issue in rough set theory. In recent years, with the fast development of data processing tools, information systems may increase quickly in objects over time. How to update attribute reducts efficiently becomes more and more important. Although some approaches have been proposed, they are used for complete decision systems. There are relatively few studies on incremental attribute reduction for incomplete decision systems. We introduce knowledge granularity, that can be obtained by the tolerance classes, to measure the uncertainty in incomplete decision systems. Furthermore, we propose incremental attribute reduction algorithms for incomplete decision systems when adding multiple objects and when deleting multiple objects, respectively. Finally, experimental results show that the proposed incremental approach is effective and efficient to update attribute reducts with the variation of objects in incomplete decision systems.