Handling Inconsistency of Vague Relations with Functional Dependencies

Vague information is common in many database applications due to internet-scale data dissemination, such as those data arising from sensor networks and mobile communications. We have formalized the notion of a vague relation in order to model vague data in our previous work. In this paper, we utilize Functional Dependencies (FDs), which are the most fundamental integrity constraints that arise in practice in relational databases, to maintain the consistency of a vague relation. The problem we tackle is, given a vague relation r over a schema R and a set of FDs F over R, what is the “best” approximation of r with respect to F when taking into account of the median membership (m) and the imprecision membership (i) thresholds. Using these two thresholds of a vague set, we define the notion of mi-overlap between vague sets and a merge operation on r. Satisfaction of an FD in r is defined in terms of values being mi-overlapping. We show that Lien’s and Atzeni’s axiom system is sound and complete for FDs being satisfied in vague relations. We study the chase procedure for a vague relation r over R, named VChase(r, F ), as a means to maintain consistency of r with respect to F . Our main result is that the output of the procedure is the most object-precise approximation of r with respect to F . The complexity of VChase(r, F ) is polynomial time in the sizes of r and F .