Uncertainty measures of rough sets based on discernibility capability in information systems

Rough set theory (RST) has been widely used to measure and handle uncertain information; however, the existing RST-based measures are difficult to generalize the results of incomplete information systems to complete information systems. In this paper, some well-justified measures of uncertainty based on discernibility capability of attributes are presented. We first define two single measures and give their useful properties, based on which a new uncertainty measure of rough sets is proposed, which can be consist with human cognition. We then propose three combination measures for multiattribute case and discuss their relationships. Last, we compare our methods with the existing measures to illustrate the physical meaning of the existing measures in RST. Theoretical analysis with numerical examples proves that the new measures will work efficiently on both complete and incomplete information systems. The research results may lead us to a deeper understanding of the essence of uncertainty.