Multiple granulation rough set approach to ordered information systems

With granular computing point of view, the classical dominance-based rough set model is based on a single granulation. For an ordered information system, this paper proposes two new types of multiple granulation rough set (MGRS) models, where a target concept is approximated from different kinds of views by using dominant classes induced by multiple granulations. And a number of important properties of the two types of MGRS are investigated in an ordered information system. From the properties, it can be found that Greco's rough set model is a special instance compared to our MGRS model. Moreover, the relationships and differences are discussed carefully among Greco's rough set and two new types of MGRS. Furthermore, several important measures are presented in two types of MGRS models, such as rough measure, quality of approximation in an ordered information system. In order to illustrate our MGRS models in an ordered information system, a real life example is considered, which is helpful for applying this theory in practical issues. One can see get that the research is meaningful in applications for the issue of knowledge reduction in complex ordered information systems.