Generalized multilayer granulation and approximations

Information (knowledge) granulation and approximations seem to be very important issues for computing science, and there are fast growing and renewed interests in this topic. The multilayer granulation structures, which have been discussed before, are all defined by a nested sequence of partitions or coverings. In the context of rough set theory, this paper proposes a generalized multilayer granulation, which is not necessary to be nested. A quasi-order relation on FC(U) is defined, where FC(U) is the collection of all the coverings of the universe. A pair of lower and upper approximations is defined and the approximation structure is investigated.