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Most of the works in mining generalized association rules under fuzzy taxonomies are focused on the pre-processing stage, using the concept of extended transactions. A great problem of these transactions is related to the generation of huge amount of candidates. Beyond that, the inclusion of ancestors in database transactions ends up generating redundancy problems. Besides, it is possible to see that many works have directed for the question of mining fuzzy rules, exploring linguistic terms, but few approaches have explored new steps of mining process. In this sense, this paper proposes the FOntGAR (Fuzzy Ontology-based Generalized Association Rules Algorithm), a new algorithm for mining generalized association rules under all levels of fuzzy concept ontologies. In this work the generalization is made during a post-processing stage. Other relevant points of this paper are the specification of a new approach of generalization; including a new grouping rules treatment, and a new and efficient way for calculating both support and confidence of generalized rules.