Updating multigranulation rough approximations with increasing of granular structures

Dynamic updating of the rough approximations is a critical factor for the success of the rough set theory since data is growing at an unprecedented rate in the information-explosion era. Though many updating schemes have been proposed to study such problem, few of them were carried out in a multigranulation environment. To fill such gap, the updating of the multigranulation rough approximations is firstly explored in this paper. Both naive and fast algorithms are presented for updating the multigranulation rough approximations with the increasing of the granular structures. Different from the naive algorithm, the fast algorithm is designed based on the monotonic property of the multigranulation rough approximations. Experiments on six microarray data sets show us that the fast algorithm can effectively reduce the computational time in comparison with the naive algorithm when facing high dimensional data sets. Moreover, it is also shown that fast algorithm is useful in decreasing the computational time of finding both traditional reduct and attribute clustering based reduct.