A unified information measure for general binary relations

Shannon's entropy and its variants have been applied to measure uncertainty in a variety of special binary relations. However, few studies have been conducted on uncertainty of general binary relations. In this study, we present a unified form of uncertainty measures for general binary relations. We redefine the concepts of entropy, joint entropy, conditional entropy, and mutual information. These uncertainty measures are generalizations of corresponding measures of special relations. We study the relationship between these measures and examine important properties. Finally, numerical experiments are performed to identify applications of the proposed uncertainty measures. Comparing with existing uncertainty measures, the proposed method not only addresses the uncertainty of heterogeneous data sets, but also exhibit better performance in attribute reduction. This study can provide a fundamental framework for uncertainty theories of special rough set models.