An extended version of the fuzzy relational database model

Abstract

The fuzzy relational database model proposed by Buckles and Petry is a formal method for organizing and using fuzzy information in relational databases. The model possesses two key properties that hold for classical relational databases: no two tuples have identical interpretations and each relational algebra operation has a unique result. The original fuzzy relational database model was based on similarity relations which were defined on finite scalar domains. Buckles and Petry later extended the model to incorporate fuzzy number domains; this extension was done without loss of consistency with the representation or the relational algebra. In a recent paper we have extended the original model to proximity relations which generalize similarity relations; the key properties of Buckles and Petry's model are preserved in the extension. In this work we demonstrate that the existence of partitions on finite scalar domains in the fuzzy relational model is the key to preserving the important properties of the classical relational model. We explain how proximity relations defined on finite scalar domains are used to partition the domains. Further, we show that normal fuzzy sets can be employed as domain values. These fuzzy sets become members of fi nite scalar domains and their characteristic functions are employed in generating the proximity relations of the fuzzy relational database model.