Dependencies in fuzzy databases: functional dependency

Classical and fuzzy functional dependencies, which consist of an important class of constraints, are examined in fuzzy relational databases. The truth value of a proposition expressing a functional dependency is not a binary value even for a classical functional dependency in fuzzy relational databases. Each tuple has a compatibility degree with a functional dependency degree which is contained in the interval [0, 1]. In each tuple it is determined by the comparison of the compatibility degree with the value of membership attribute whether that tuple satisfies the functional dependency. This means that the functional dependency is dealt with in the same manner as the other constraints. Armstrong's inference rules are sound and complete for classical functional dependencies as well as in relational databases, but they are not for fuzzy functional dependencies. Sound and complete inference rules different from Armstrong's ones hold for fuzzy functional dependencies. >