An equivalence classes model of fuzzy relational databases

Abstract

The technique of employing sets of values for tuple components to express imprecision in relational databases was proposed by Buckles and Petry in their classic works on fuzzy relational databases. In addition to providing an intuitively appealing scheme for representing fuzzy information, the model of Buckles and Petry possesses several key properties of the classical relational model. By employing finite scalar domains with similarity relations and special fuzzy number domains, Buckles and Petry have demonstrated that the classical properties of uniqueness of tuple interpretations and well-definedness of the relational algebra can be retained in the fuzzy relational database model. The key to the preservation of these properties is the fact that scalar domains with similarity relations and the fuzzy number domains can be partitioned into equivalence classes. However, since equivalence classes can be constructed without assuming the existence of similarity relations or special fuzzy number domains, it is desirable to generalize the fuzzy relational database model to one based only on equivalence classes. In this work we show that the important properties of classical relational databases (and of fuzzy relational databases) are preserved in a generalized model built on equivalence relations on finite database domains. Further, we generalize the notion of a functional dependency to the fuzzy relational model.