Functional dependencies and normal forms in the fuzzy relational database model

Abstract

The fuzzy relational database model as defined by Buckles and Petry employs sets in place of atomic values for components of tuples in database relations. This technique for dealing with imprecision in relational databases is intuitively appealing. Moreover, the model preserves several important properties of classical relational databases. In recent works we have demonstrated that the existence of partitions on scalar domains is the key to ensuring conformity with the classical relational model. Specifically, by restricting the components of fuzzy tuples to be nonempty subsets of equivalence classes from domain partitions, it is possible to define the notions of redundant tuples and consistent database relations and to specify a well-defined fuzzy relational algebra. Since these properties are obtained by working only with equivalence classes, the fuzzy relational model of Buckles and Petry is generalized to an equivalence classes model of relational databases. In this work, additional properties of the fuzzy relational database model are presented. By employing equivalence classes from domain partitions, we define functional dependencies and normal forms for the fuzzy relational model. These definitions extend the corresponding classical definitions. Moreover, our definitions of functional dependencies and normal forms provide valuable guidelines for designing fuzzy relational databases.