Distance: A more comprehensible perspective for measures in rough set theory

Distance provides a comprehensible perspective for characterizing the difference between two objects in a metric space. There are many measures which have been proposed and applied for various targets in rough set theory. In this study, through introducing set distance and partition distance to rough set theory, we investigate how to understand measures from rough set theory in the viewpoint of distance, which are inclusion degree, accuracy measure, rough measure, approximation quality, fuzziness measure, three decision evaluation criteria, information measure and information granularity. Moreover, a rough set framework based on the set distance is also a very interesting perspective for understanding rough set approximation. From the view of distance, these results look forward to providing a more comprehensible perspective for measures in rough set theory. 2011 Elsevier B.V. All rights reserved.