Extracting compact and information lossless sets of fuzzy association rules

Applying classical association rule extraction framework on fuzzy datasets leads to an unmanageably highly sized association rule sets. Moreover, the discretization operation leads to information loss and constitutes a hamper towards an efficient exploitation of the mined knowledge. To overcome such a drawback, this paper proposes the extraction and the exploitation of compact and informative generic basis of fuzzy association rules. The presented approach relies on the extension, within the fuzzy context, of the notion of closure and Galois connection, that we introduce in this paper. In order to select without loss of information a generic subset of all fuzzy association rules, we define three fuzzy generic basis from which remaining (redundant) FARs are generated. This generic basis constitutes a compact nucleus of fuzzy association rules, from which it is possible to informatively derive all the remaining rules. In order to ensure a sound and complete derivation process, we introduce an axiomatic system allowing the complete derivation of all the redundant rules. The results obtained from experiments carried out on benchmark datasets are very encouraging. They highlight a very important reduction of the number of the extracted fuzzy association rules without information loss.