Fuzzy Extensions of Rough Approximations Based on Relations

This paper mainly focus on the fuzzy rough approximation operators based fuzzy relations. Three types of rough approximation operators based on crisp relations are reviewed. Based on their composition properties, two types of them are generalized in fuzzy approximation space. Subsequently, some properties of the derived fuzzy rough fuzzy approximation operators are examined in detail. By comparing three pairs of fuzzy approximation operators based on fuzzy relations, some conditions are obtained, under which some or all of them are equivalent.