On Soundness of Various Inference Rules for Vague Functional Dependencies

In this paper we complement the most recent results on soundness of inference rules for new vague multivalued dependencies. Motivated by the fact that the inclusive and the augmentation rules are sound, we prove that: complementation, transitivity, replication, coalescence, union, pseudo-transitivity, decomposition, and mixed pseudo-transitivity rules are also sound. Our research relies on definitions of vague functional and vague multivalued dependencies based on appropriately selected similarity measures between vague values, vague sets, and tuples on sets of attributes.