Analysis of fuzzy -ary relations with the use of interval-valued fuzzy functional dependencies

Abstract

The paper contains an analysis of integrity constraints for -ary relations in fuzzy databases. Apart from dependencies between all attributes there may be also dependencies describing relationships of fewer attributes. However, there is no complete arbitrariness. Relationships comprising (1) attributes must not infringe integrity constraints of the -ary relation. The analysis is carried out using the theory of functional dependencies. In this paper, we assume that attribute values are represented by means of interval-valued possibility distributions. The notion of fuzzy functional dependency has been appropriately extended according to the representation of fuzzy data. The paper formulates the rules to which fuzzy functional dependencies between (1) attributes of the -ary relation must be subordinated.

Keywords:

• fuzzy databases
• interval-valued fuzzy sets
• fuzzy functional dependencies
• fuzzy normal forms
• possibility distribution
• n-ary relations