A complete axiomatization for fuzzy functional and multivalued dependencies in fuzzy database relations

This paper first introduces the formal definitions of fuzzy functional and multivalued dependencies which are given on the basis of the conformance values presented here. Second, the inference rules are listed after both fuzzy functional and multivalued dependencies are shown to be consistent, that is, they reduce to those of the classic functional and multivalued dependencies when crisp attributes are involved. Finally, the inference rules presented here are shown to be sound and complete for the family of functional and multivalued dependencies in fuzzy database relations.