Information granules in general and complete coverings

Two different operations of information granules are defined in the general coverings on a universe in this paper and different levels of granularity of coverings are studied based on the operations. Besides, general covering and complete covering according to a compatible relation are established in rough set theory in incomplete information systems, respectively. Complete covering is compared with general covering and then a necessary and sufficient theorem is proved to ensure a covering to be a complete covering. Some other significant results are also gained.