Rough set theory emerged in the 1980s to provide alternative tools for dealing with vague concepts. A rough set is a representation of a crisp set in terms of two crisp subsets—the lower and upper approximation of the set.

Accuracy measures are used to quantify the imprecision imposed by the boundary regions of the rough sets. Standard approaches do not successfully account for the granularity of the partitions that an equivalence relation induces. Using information theory tools and measures, Xu, Zhou, and Lu propose an excess entropy-based accuracy measure that accounts for it.

The authors define an equivalence relation graph that is used as an information source, compute its entropy, and use the excess entropy (the entropy of joint sources is less than or equal to the sum of the entropy of individual sources) to represent the connectivity between the nodes in the graph. The quotient between that excess and the excess in the complete corresponding graph is used as a measure of roughness of a set.

This paper is very easy to follow, as it introduces the concepts methodically and the given examples help a reader comprehend the concepts being described. The authors have done a good job of presenting a successful infusion of concepts from one discipline (information theory) into another (rough sets).