This paper represents a natural continuation of our previous study. In our earlier research we proved that the inclusive inference rule and the union inference rule for new vague functional dependencies are sound, and sketched a proof of the fact that the set of the main inference rules is a complete set. In the present paper we rigorously prove that: reflexive, augmentation, transitivity, pseudo-transitivity, and decomposition inference rules are also sound. Some additional insights in completeness of the main inference rules are also provided.

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.

Klir-Yuan fuzzy implication, as fuzzy implication generated from the standard strong fuzzy negation, the probabilistic sum t-conorm, and the product t-norm, represents a classical example of QL-implication, where QL-implications are the short for quantum logic fuzzy implications. In this paper we prove that the recent results on equivalences between fuzzy formulas and fuzzy dependencies remain invariant with respect to QL-implications when considered through Klir-Yuan fuzzy implication.

In the present paper we give a new definition of vague multivalued dependencies in database relations. The definition is based on application of arbitrary similarity measure on vague values, which is known to be reflexive, symmetric, and max-min transitive. The definition is adapted in order to include the imprecise and precise vague multivalued dependencies. The inference rules for new vague multivalued dependencies are listed, and are shown to be sound.

In this paper we introduce a new definition of vague functional dependency based on application of appropriately chosen similarity measures. The definition is adjusted in order to be applicable to both, the imprecise and precise vague functional dependencies. Ultimately, the set of inference rules for new vague functional dependencies is given, and is proven to be sound and complete.

A fuzzy formula does not necessarily follow from a set of fuzzy formulas. In the case when fuzzy formulas and fuzzy dependencies are mutually identified, the corresponding equivalent statement has an obvious meaning. An affirmative statement, however, rises the question of automatization. In our earlier research, we offered an efficient algorithm based on application of selected fuzzy logic operators and resolution principle. In this paper we prove that those ingredients of the algorithm that explicitly depend on the choice of fuzzy implication operator, hold also true for the class of g-generated fuzzy implications.