Abstract
Uncertainty measures are an important tool for analyzing data. There is the uncertainty of a rough set caused by its boundary region in rough set models. Thus the uncertainty measurement issue is also an important topic for rough set theory. Shannon entropy has been introduced into rough set theory. However, there are relatively few studies on the uncertainty measure in generalized rough set models. We know that the boundary region of a rough set is closely related to the upper and lower approximations in rough set models. In this paper, from the viewpoint of the upper and lower approximations, we propose new uncertainty measures, the upper rough entropy and the lower rough entropy, in generalized rough set models. Then we focus on the investigations of the upper rough entropy, and give the concepts of the upper joint entropy, the upper conditional entropy and the mutual information with respect to a general binary relation. Some important properties of these measures are obtained. The connections among these measures are given. Furthermore, comparing with the existing uncertainty measures, the upper rough entropy has high distinguishing degree. Theoretical analysis and experimental results show that the proposed entropy is better effective than some existing measures.