Set-valued information systems are generalized models of single-valued information systems. The attribute set in the set-valued information system may evolve over time when new information arrives. Approximations of a concept by rough set theory need updating for knowledge discovery or other related tasks. Based on a matrix representation of rough set approximations, a basic vector H(X) is induced from the relation matrix. Four cut matrices of H(X), denoted by H^[μ,ν](X), H^(μ,ν](X), H^[μ,ν)(X) and H^(μ,ν)(X), are derived for the approximations, positive, boundary and negative regions intuitively. The variation of the relation matrix is discussed while the system varies over time. The incremental approaches for updating the relation matrix are proposed to update rough set approximations. The algorithms corresponding to the incremental approaches are presented. Extensive experiments on different data sets from UCI and user-defined data sets show that the proposed incremental approaches effectively reduce the computational time in comparison with the non-incremental approach.