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As we all known, dynamic updating of rough approximations and reducts are keys to the applications of the rough set theory in real data sets. In recent years, with respect to different requirements, many approaches have been proposed to study such problems. Nevertheless, few of the them are carried out under multigranulation fuzzy environment. To fill such gap, the updating computations of multigranulation fuzzy rough approximations are explored in this paper. By considering the dynamic increasing of fuzzy granular structures, which are induced by fuzzy relations, naive and fast algorithms are presented, respectively. Moreover, both naive and fast forward greedy algorithms are designed for granular structure selection in dynamic updating environment. Experiments on six data sets from UCI show that fast algorithms are more effective for reducing computational time in comparison with naive algorithms.