All-Monotony: A Generalization of the All-Confidence Antimonotony

Many studies have shown the limits of support/confidence framework used in Apriori-like algorithms to mine association rules. One solution to cope with this limitation is to get rid of frequent itemset mining and to focus as soon as possible on interesting rules. Many works have focused on the algorithmic properties of the confidence. In particular, the all-confidence which is a transformation of the confidence, has the antimonotone property. In this paper, we generalize the all-confidence by associating to any measure its corresponding all-measure. We present a formal framework which allows us to make the link between analytic and algorithmic properties of the all-measure. We then propose the notion of all-monotony which corresponds to the monotony property of the all-measures. Our results show that although being very interesting, all-monotony is a demanding property.