Multi-granulation fuzzy rough set model on tolerance relations

Based on the analysis of rough set model on a tolerance relation and considering of the theory of fuzzy rough set, two types of new generalized fuzzy rough set models are constructed, which are multi-granulation fuzzy rough sets 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 on tolerance relations. The fuzzy rough set model and rough set model on a tolerance relation are special cases of the new one from the perspective of the considered concepts and granular computing. The relationships among the fuzzy rough set model, the first MGFRS and the second MGFRS all on tolerance relations are investigated.