On Completeness of Inference Rules for Vague Functional and Vague Multivalued Dependencies in Two-Element Vague Relation
In this paper we pay attention to completeness of the inference rules for vague functional and vague multivalued dependencies in two-element, vague relation instances. Motivated by the fact that the set of the inference rules is a complete set, that is, these exists a vague relation instance on given relation scheme which satisfies all vague functional and vague multivalued dependencies in the closure of the union of some set of vague functional and some set of vague multivalued dependencies, and violates a vague functional, respectively, a vague multivalued dependency outside of the closure, we prove that the vague relation instance may be chosen to contain only two elements.