New and improved: grey multi-granulation rough sets

Rough set has drawn great attention in recent decades, among which multi-granulation rough set (MGRS) is an arresting direction. It constructs a formal theoretical framework to solve complex problems under the circumstance of multiple binary relations. However, the fusion of multi-granulation rough set and grey system for acquiring knowledge is still a gap. Toward this end, we devise a grey multi-granulation rough set (GMGRS) by taking multiple grey relational relations into consideration under the framework of MGRS. In grey information system, the constructed grey relational relation that measures the relationship among objects can be used to further establish multiple binary relations. Based on two different approximate strategies (seeking common reserving difference and seeking common eliminating difference), two types of GMGRS are presented, respectively. After discussing several important properties of GMGRS, we discover that the properties of the proposed GMGRS are synchronous with the classical MGRS. Meanwhile, to obtain the attribute reduction under GMGRS, we reconstruct significance measure and termination criterion based on the theta-precision pessimistic GMGRS. Last but not least, theoretical studies and practical examples demonstrate that our proposed GMGRS largely enrich the MGRS theory and provide a new technique for knowledge discovery, which is practical in real-world scenarios.