This paper discusses the so-called missing data problem, i.e. the problem of imputing missing values in information systems.A new algorithm, called the ARSI algorithm, is proposed to address the imputation problem of missing values on categorical databases using the framework of rough set theory.This algorithm can be seen as a refinement of the ROUSTIDA algorithm and combines the approach of a generalized non-symmetric similarity relation with a generalized discernibility matrix to predict the missing values on incomplete information systems.Computational experiments show that the proposed algorithm is as efficient and competitive as other imputation algorithms.