Narrow Results

The implication of multivalued dependencies (MVDs) in relational databases has originally and independently been defined in the context of some fixed finite universe by Delobel, Fagin, and Zaniolo. Biskup observed that the original axiomatisation for MVD implication does not reflect the fact that the complementation rule is merely a means to achieve database normalisation. He proposed two alternative ways to overcome this deficiency: i) an axiomatisation that does represent the role of the complementation rule adequately, and ii) a notion of MVD implication in which the underlying universe of attributes is left undetermined together with an axiomatisation of this notion.

In this paper we investigate multivalued dependencies with null values (NMVDs) as defined and axiomatised by Lien. We show that Lien's axiomatisation does not adequately reflect the role of the complementation rule, and extend Biskup's findings for MVDs in total database relations to NMVDs in partial database relations. Moreover, a correspondence between (minimal) axiomatisations in fixed universes that do reflect the property of complementation and (minimal) axiomatisations in undetermined universes is shown.

The relationship between the absence of redundancy in relational databases and fourth normal form (4NF) is investigated. A relation scheme is defined to be redundant if there exists a legal relation defined over it which has at least two tuples that are identical on the attributes in a functional dependency (FD) or multivalued dependency (MVD) constraint. Depending on whether the dependencies in a set of constraints or the dependencies in the closure of the set is used, two different types of redundancy are defined. It is shown that the two types of redundancy are equivalent and their absence in a relation scheme is equivalent to the 4NF condition.

In this paper we discuss an important integrity constraint called multivalued dependency (mvd), which occurs as a result of the first normal form, in the framework of a newly proposed model called fuzzy multivalued relational data model. The fuzzy multivalued relational data model proposed in this paper accommodates a wider class of ambiguities by representing the domain of attributes as a “set of fuzzy subsets”. We show that our model is able to represent multiple types of impreciseness occurring in the real world. To compute the equality of two fuzzy sets/values (which occur as tuple-values), we use the concept of fuzzy functions. So the main objective of this paper is to extend the mvds in context of fuzzy multivalued relational model so that a wider class of impreciseness can be captured. Since the mvds may not exist in isolation, a complete axiomatization for a set of fuzzy functional dependencies (ffds) and mvds in fuzzy multivalued relational schema is provided and the role of fmvds in obtaining the lossless join decomposition is discussed. We also provide a set of sound Inference Rules for the fmvds and derive the conditions for these Inference Rules to be complete. We also derive the conditions for obtaining the lossless join decomposition of a fuzzy multivalued relational schema in the presence of the fmvds. Finally we extend the ABU's Algorithm to find the lossless join decomposition in context of fuzzy multivalued relational databases. We apply all of the concepts of fmvds developed by us to a real world application of “Technical Institute” and demonstrate that how the concepts fit well to capture the multiple types of impreciseness.