Fuzzy Functional Dependency and the Resolution Principle

Article type: Research Article

Authors: Dukić, Nedzad | Avdagić, Zikrija

Affiliations: Faculty of Science, Department of Mathematic, University of Sarajevo, Bosnia and Herzegovina, e‐mail: ndukic@pmf.unsa.ba | Faculty of Electrical Engineering, University of Sarajevo, Bosnia and Herzegovina, e‐mail: ndukic@pmf.unsa.ba

Abstract: In this paper we establish equivalence between a theory of fuzzy functional dependences and a fragment of fuzzy logic. We give a way to interpret fuzzy functional dependences as formulas in fuzzy logic. This goal is realized in four steps. Truth assignment of attributes is defined in terms of closeness between two tuples in a fuzzy relation. A corresponding fuzzy formula is associated to a fuzzy functional dependence. It is proved that if a relation satisfies a fuzzy functional dependence, then the corresponding fuzzy formula is satisfied and vice verse. Finally, equivalence of a fuzzy formulas and a set fuzzy functional dependence is demonstrated. Thus we are in position to apply the rule of resolution from fuzzy logic, while calculating fuzzy functional dependences.

Keywords: fuzzy relation database, fuzzy functional dependency, fuzzy logic, resolution

Journal: Informatica, vol. 16, no. 1, pp. 45-60, 2005