The large amount of association rules resulting from a KDD process makes the exploitation of the patterns embedded in the database difficult even impossible. In order to address this problem, various interestingness measures were proposed for selecting the most relevant rules. Nevertheless, the choice of an appropriate measure remains a hard task and the use of several measures may lead to conflicting information. In this paper, we propose a unified framework for a set of interestingness measures
and prove that most of the usual objective measures behave in a similar way. In the context of classification rules, we show that each measure of
admits a lower bound on condition that a minimal frequency threshold and a maximal number of exceptions are considered. Furthermore, our framework enables to characterize the whole collection of the rules simultaneously optimizing all the measures of
. We finally provide a method to mine a rule cover of this collection.