The notion of flexible queries covers different meanings depending on the authors. Here, it is assumed to stand for queries involving preferences and the fuzzy set framework is advocated as a general tool for supporting the expression of preferences. If fuzzy queries can apply to regular databases where information stored is precisely known, one can wonder about the case where the database contains some ill-known data (represented as possibility distributions) and this issue is the heart of the paper. Two significantly different approaches are suggested. In the first one, any condition concerns the values themselves and its interpretation is based on a fuzzy pattern matching mechanism. Then, the answer of a query is uncertain, i.e., any element is associated with a possibility and a necessity degree. In the second approach, a condition relates to the representation of values, and, as such, returns a truth value which is certain.