In association rules mining, current trend is witnessing the emergence of a growing number of works toward bringing negative items to light in the mined knowledge. However, the amount of the extracted rules is huge, thus not feasible in practice. In this paper, we propose to extract a subset of generalized association rules (i.e., association rules with negation) from which we can retrieve the whole set of generalized association rules. Results of experiments carried out on benchmark databases showed important prots in terms of compactness of the introduced generic basis.