A Hybrid Relational Database Model for Uncertain and Imprecise Information

Abstract

Recent years, many fuzzy or probabilistic database models have been built for representing and handling imprecise or uncertain information of objects in real-world applications. However, relational database models combining the relevance and strength of both fuzzy set and probability theories have rarely been proposed. This paper introduces a new relational database model, as a hybrid one combining consistently fuzzy set theory and probability theory for modeling and manipulating uncertain and imprecise information, where the uncertainty and imprecision of a relational attribute value are represented by a fuzzy probabilistic triple, the computation and combination of relational attribute values are implemented by using the probabilistic interpretation of binary relations on fuzzy sets, and the elimination of redundant data is dealt with by coalescing e-equivalent tuples. The basic concepts of the classical relational database model are extended in this new model. Then the relational algebraic operations are formally defined accordingly. A set of the properties of the relational algebraic operations is also formulated and proven.