Optimistic Multi-Granulation Fuzzy Rough Sets on Tolerance Relations

Based on the analysis of rough set model on a tolerance relation and the theory of fuzzy rough set, a new extended rough set model is constructed, which is the optimistic multi-granulation fuzzy rough sets based on tolerance relations. It follows the research on the properties of the lower and upper approximations of the new multi-granulation fuzzy rough set models based on tolerance relations. From which it can be found that the new extended model is a generalized rough set model based on tolerance relations from the perspective of granulation.