The paper proposes an ontology alignment framework with two core features: the use of background knowledge and the ability to handle imprecision in the matching process and the resulting concept alignments. The procedure is based on the use of a generic reference vocabulary, which is used to define an explicit semantic space for the ontologies to be matched. General-purpose background knowledge sources based on Wikipedia, such as Yago, appear to be appropriate choices of reference vocabularies. The outcome of the procedure is a combined fuzzy knowledge body which captures what is common in two source ontologies. The proposed approach allows to discover cross-concept relations of the kind many-to-many. An important application of the method is found in the field of cross-lingual ontology matching.