A binary granule representation for uncertainty measures in rough set theory

Uncertainty measures can supply new points of view for analyzing data and help us to disclose the substantive characteristics of data sets. Accuracy and roughness proposed by Pawlak are mainly two important measures to deal with uncertainty information in rough set theory. However, these measures are constructed by set operations, which bring about poor efficiency. In this paper, we proposed a binary granule representation by a conversion from a set to a binary granule. Correspondingly, set operations are converted to binary granule computing. Besides, we investigate how to understand measures from rough set framework in the viewpoint of binary granule representation by introducing Hamming distance between granules. Moreover, a concept of granule swarm distance is defined for measuring uncertainty between two granule swarms, which provides a more comprehensible perspective for measures in rough set theory. Theoretical analysis shows that the binary granule representation is valuable to understand rough set measures.