Matroidal structure of covering rough sets based on multigranulation

Multigranulation rough sets provide an effective way to extend the classical rough sets based on single granulation to multigranulation. Covering rough set is a generalisation of classical rough set. This paper extends single granulation matroid to multigranulation matroid based on covering rough set. On one hand, we construct a multigranulation matroid through union of several independent sets. Then we define a multigranulation rank function from many single granulation rank functions. Moreover, a pair of multigranulation matroid approximation operators are described by the multigranulation rank function and properties of these approximation operators are studied. We present the relationship between the multi-granulation matroid approximations and the multigranulation approximations in rough set model. On the other hand, we propose a dual multigranulation matroid. Furthermore, the multigranulation rank function and multigranulation approximation operator of the dual multigranulation matroid are obtained.