From the mapping relationship between information vector matrix and relative vectors, rough approximation, attribute relative reductions and selecting optimal attribute reductions set algorithms based on binary vector matrix were proposed. Inconsistency of acquiring attribute kernel and blindness of selecting attribute reductions are overcome. On the foundation of studying binary vector matrix algorithms, binary vector compression matrix algorithm was also put forward, and the algorithm complexity was decreased faster than the original matrix algorithm. By the example analysis, the validity of the proposed algorithms was verified, the feasible computing way is presented for studying rough set further.  

Rough set,    , Binary vector matrix,    , Attribute reductions,    , Information compression