(0,1)-Qualitative approximations of fuzzy sets are studied by using the core and support of a fuzzy set. This setting naturally leads to three disjoint regions and an analysis based on a three-valued logic. This study combines both an algebra view and a logic view. From the algebra view, the mathematical definition of a (0,1)-approximation of fuzzy sets are given, and algebraic operations based on various
-norms and fuzzy implications are established. From the logic view, a non-classical three-valued logic is introduced. Corresponding to this new non-classical three-valued logic, the related origins of
-norms and fuzzy implications are examined.