Summary: This paper proposes an approach to the tolerant rewriting of queries in terms of views when the views and the queries may involve fuzzy value constraints in the context of a Local-As-View mediation system. These constraints describe attribute values as a set of elements attached with a degree in $[0,\:1]$ that expresses the plausibility attached to a given element, i.e., attribute values more or less plausible/typical in the views, while in the queries, they denotes preferences, i.e., more or less desired values. The problem of rewriting queries is formalized in the setting of the description logic ${\cal FL}_0$ extended to fuzzy value constraints. We propose an algorithm of gradual and structural subsumption for this extended logic, that plays a key role in the query rewriting algorithm. Finally, we characterize the tolerant query rewriting forms and propose an algorithm to compute them.