Conditions with aggregates evaluated using gradual numbers

This paper is devoted to the evaluation of conditions involving aggregates in the context of flexible querying of relational databases. An example of such a condition is “the maximum salary of young employees is high”, where the aggregate max applies to a fuzzy set of salaries. At first, we consider the evaluation of quantified statements where the aggregate count (the cardinality) is implicitly used. We extend this result to conditions involving the aggregates average, maximum or minimum. The contribution of this paper is to propose a new theoretical background for their evaluations based on an arithmetic on gradual numbers (Nf ,Zf ,Qf ).