Evaluating aggregates in possibilistic relational databases

The need for extending information management systems to handle the imprecision of information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature has dealt with queries involving a functional evaluation of a set of items, traditionally referred to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applications , and thus this paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, speciically, aggregates within vague queries on precise data, aggregates within precisely speciied queries on pos-sibilistic data, and aggregates within vague queries on imprecise data. The consistency of the proposed operations is shown. An extended operator is deened to be consistent if it defaults to its classical counterpart when evaluated on crisp data.