An extended relational database model and algebra with interval probability valued attributes and tuples

Abstract

This paper introduces an extended relational database model and algebra, named EPRDB, where both the attribute and tuple of a relation may take values associated with interval probabilities for modelling and computing uncertain and imprecise information. To build EPRDB, three key methods are employed: i) probabilistic values and intervals are used for representing uncertain and imprecise valued attributes and tuple membership degrees; ii) the probabilistic interpretations of binary relations on sets and operators on probability intervals are proposed for computing and querying the uncertain degree of relations on value domains of attributes; and iii) the combination strategies of probabilistic intervals and values are defined for manipulating probabilistic relational tuples. Then, the EPRDB data model including fundamental concepts and components such as the schema, probabilistic relation, functional dependency, and key is extended with interval probability valued attributes and tuples such that it is coherent and consistent with the classical relational data model. The EPRDB algebra including the set of basic probabilistic relational algebraic operations is developed corresponding to the EPRDB data model. A set of the properties of the algebraic operations is also formulated and proven. The new proposed EPRDB model and algebra can represent and deal effectively with uncertain and imprecise information in practical applications.