Fuzzy Description Logics DLs are logics that allow to deal with structured vague knowledge. Although a relatively important amount of work has been carried out in the last years concerning the use of fuzzy DLs as ontology languages, the problem of automatically managing the evolution of fuzzy ontologies has received very little attention so far. We describe here a logic-based computational method for the automated induction of fuzzy ontology axioms which follows the machine learning approach of Inductive Logic Programming. The potential usefulness of the method is illustrated by means of an example taken from the tourism application domain.