Z. Supp and . ?t, Par ailleurs, Conf(Z?T ) = Conf(X?Y ) donc Supp(T )(1??)+? ? Conf(Z?T ) < 1. Alors, encore par la Proposition 50, ? ? M GK (Z?T ) < 1, ce qui démontre que Z?T est approximative (M GK , ?)-valide. Par ailleurs, nous avons le résultat suivant

M. Gk, 1 alors ?(X)??(Y ) est unélémentunélément de BPA(?) Par ailleurs, l'application de (PA) ` a Z?T donne la r` egle X?Y . Montrons maintenant que BPA(?) est minimal. Soit X? Y unélémentunélément de BPA(?) et soit BPA (?) = BPA(?) ? {X?Y }. Nous montrons que la r` egle X?Y ne peut pasêtrepasêtre dérivée de BPA (?) par application (PA) En effet, si X?Y pouvaitêtrepouvaitêtre dérivée de BP A (?), alors, il existerait une suite finie de r` egles d'association X 1 ?Y 1

A. Est-une-r-`-egle-de-la-base and B. A. , 6 ) Par application de l'axiome d'inférence (PA), nous pouvons dériver les neuf r` egles d'association A?AB

L. Bases, B. A. , and B. A. , Ensuite, les ensembles FC i sont parcourus successivement dans l'ordre décroissant (ou croissant) de i (lignes 2` a 21) Durant une itération i, ` a partir de tout motif fermé Y il y a deuxétapesdeuxétapes : (a) l'algorithme construit une partie de la base BP A ` a partir des fermés qui sont sous motifs de Y

L. Tableau and 7. , 7 présente les nombres de r` egles dans les bases ainsi que ceux de toutes les r` egles M GK -valides, selon les quatre types de r` egles que nous considérons dans ce travail

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