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.
Highlights
According to the classical relation database all the information in it, have to involve precisely defined values
For a set of fuzzy dependencies F and single fuzzy functional dependency f, we show that F implies f as fuzzy functional dependencies if and only if F implies f under the logic interpretation
Lets prove in two ways that this examples holds, using following a) calculus of fuzzy functional dependences. b) the resolution principle in fuzzy logic
Summary
According to the classical relation database all the information in it, have to involve precisely defined values (atomic). The other way of considering this imprecise information is the involving of fuzzy value to the domain of attribute. These imprecise information have been focused on Zadeh’s fuzzy set theory and fuzzy logic. Approaches to representation of inexact information in relation database theory, include fuzzy membership values (Buckles and Petry, 1982a; Chen, 1998; Zadeh, 1975), similarity relationships (Buckles and Petry, 1982b; Sozat and Yazici, 2001) and possibility distributions. In classic logic as in fuzzy logic there is effective procedure, which from its starting set of formulas as well as its logic consequence shows validity of given formula Such a procedure is known as the rule of resolution (Habiballa, 2000; Lee, 1972; Mukaidono, 1986). Is possible to apply the rules of deduction in fuzzy logic, on calculus of fuzzy functional dependence
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