Dependencies in fuzzy databases: multivalued dependency

Multivalued dependencies, which consist of an important class of constraints, are formulated in the same manner as other constraints in fuzzy relational databases. The compatibility degree of a tuple value with a multivalued dependency is a value contained in the interval [0,1]. Whether a tuple satisfies the multivalued dependency is determined by comparing the compatibility degree with the value of membership attribute. The formulations for a multivalued dependency, which do not contain any parameters, are addressed on the basis of two interpretations. They correspond to using Godel implication and material implication, respectively. In the interpretation corresponding to using Godel implication, extended sound and complete inference rules of the conventional ones are valid for any multivalued dependency. On the other hand, in the interpretation corresponding to using material implication, the extended inference rules are valid for multivalued dependencies with identity relations, but is not so for ones with resemblance relations. In the latter case, new sound and complete inference rules have been discovered.