Two New Types of Multiple Granulation Rough Set

In the paper proposed two new types of the multiple granulation rough set models, where a target concept is approximated from two different kinds of views by using the equivalence classes induced by multiple granulations. A number of important properties of the two types of MGRS are investigated. From the properties, it can be found that Pawlak’s and Qian’s rough set models are special instances of those of our MGRS. Moreover, several important measures are presented in two types of MGRS, such as rough measure and quality of approximation. Furthermore, the relationship and difference are discussed carefully among Pawlak’s rough set, Qian’s MGRS, and two new types of MGRS. In order to illustrate our multiple granulations rough set model, some examples are considered, which are helpful for applying this theory in practical issues. One can get that the paper is meaningful both in the theory and in application for the issue of knowledge reduction in complex information systems.