Functional Dependencies in Vague Relational Databases

In order to model the real world with imprecise and uncertain information, various extended relational data models were proposed. Vague set, as a generalized fuzzy set, has more powerful ability to process fuzzy information than fuzzy set. In this paper, we propose a kind of vague relational model and a new similarity measure between vague sets based on the set-theoretic approach. Based on the proposed similarity measure, the paper focuses on the issues of vague functional dependencies (VFDs), and then proposes a set of sound inference rules, which are similar to Armstrong´s axioms for classical case, for vague functional dependencies. Finally, the paper presents the satisfaction degree of the VFDs and the formula to determine the satisfaction degree of VFDs.