SDS-rules and association rules

The association rule expresses the relation between premise (antecedent) and consequence (succedent). The relation is given by a truth-condition, which can be verified on a given four-fold contingency table denoting the frequencies of objects in some matrix of analyzed data (not-)satisfying antecedent and succedent. This method is more general than the "classical" association rules mined by A-priori algorithm. Various types of implication or equivalency can be expressed as well as relations corresponding to statistical hypotheses tests.This notion of association rules can be modified to describe interesting relations in couples of associated disjoint sets. Let's have two Boolean attributes defining two disjoint sets A and B and the third attribute describing some property of the objects. The SDS-rule describes a relation among the sets A and B and the given property. The usual application (interpretation) is to find couples of sets that significantly differ in the given attribute or to find strong differences between given sets A and B. This paper describes the motivation of SDS-rules, similarity with association rules and introduces some SDS-quantifiers. Later it describes how to define disjoint sets A and B using derived attributes of analyzed data matrix and gives some results of this method applied to medical data.