In rough set theory (RST), upper and lower approximations of a concept will change dynamically while the information system varies over time. How to update approximations based on the original approximations' information is an important problem since it may improve the efficiency of knowledge discovery. This paper focuses on the approach for dynamically updating approximations when attribute values coarsening or refining. The definitions of attribute values coarsening and refining in information systems are introduced. The properties for dynamic maintenance of upper and lower approximations while attribute values coarsen and refine are presented. Finally, the principle of coarsening or refining of the multi-granularity attribute values is analyzed.