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Many propositions to extend database management systems have been made in the last decade. Some of them aim at the support of a wider range of queries involving fuzzy predicates. Unfortunately, these queries are somewhat complex and the question of their efficiency is a subject under discussion. In this paper, we focus on a particular subset of queries, namely those using fuzzy quantified predicates. More precisely, we will consider the case where such predicates apply to individual elements as well as to sets of elements. Thanks to some interesting properties of alpha-cuts of fuzzy sets, we are able to show that the evaluation of these queries can be significantly improved with respect to a naive strategy based on exhaustive scans of sets or files.