Evaluating aggregates in possibilistic relational databases

This paper presents a framework for handling two types of aggregate operators, namely, scalar aggregates and aggregate functions, in the context of imprecise information and considers three cases, specifically, aggregates within vague queries on precise data, aggregate within precisely specified queries on possibilistic data.

Abstract

The need for extending information management systems to handle the imprecision iof 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 had dealt with queries involving a functional evaluation of a set of items, traditionally refered to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applciations, and thus this paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. The consistency of the proposed operations is shown. An extended operator is defined to be consistent if it defaults to its classical counterpart when evaluated on crisp data.