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Minining association rules is an important problem in Knowledge Extraction (KE). This paper proposes an efficient method for mining simultaneously informative positive and negative association rules, using a new selective pair support-MGK . For this, we define four new bases of positive and negative association rules, based on Galois connetion semantics. These bases are characterized by frequent closed itemsets, maximal frequent itemsets, and their generator itemsets; it consists of the non-redundant exact and approximate association rules having minimal premise and maximal conclusion, i.e. the informative association rules. We introduce Nonred algorithm allowing to generate these bases and all valid informative association rules. Results experiments carried out on reference datasets show the usefulness of this approach.

Given a large collection of transactions containing items, a basic common association rules problem is the huge size of the extracted rule set. Pruning uninteresting and redundant association rules is a promising approach to solve this problem. In this paper, we propose a Condensed Representation for Positive and Negative Association Rules representing non-redundant rules for both exact and approximate association rules based on the sets of frequent generator itemsets, frequent closed itemsets, maximal frequent itemsets, and minimal infrequent itemsets in database B. Experiments on dense (highly-correlated) databases show a significant reduction of the size of extracted association rule set in database B.

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