  Attribute reduction is viewed as an important preprocessing step for pattern
recognition and data mining. Most of researches are focused on attribute
reduction by using rough sets. Recently, Tsang et al. discussed attribute
reduction with covering rough sets in the paper [E. C.C. Tsang, D. Chen, Daniel
S. Yeung, Approximations and reducts with covering generalized rough sets,
Computers and Mathematics with Applications 56 (2008) 279-289], where an
approach based on discernibility matrix was presented to compute all attribute
reducts. In this paper, we provide an improved approach by constructing simpler
discernibility matrix with covering rough sets, and then proceed to improve
some characterizations of attribute reduction provided by Tsang et al. It is
proved that the improved discernible matrix is equivalent to the old one, but
the computational complexity of discernible matrix is greatly reduced.
