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In this paper, we discuss an approach for relaxing a failing query in the context of flexible (or fuzzy) querying. The approach relies on the notion of a parameterized proximity relation which is defined in a relative way. We show how such a proximity relation allows for transforming a gradual predicate into an enlarged one. The resulting predicate is semantically close to the original one and it is obtained by a simple fuzzy arithmetic operation. Such a transformation provides the basis for a flexible query relaxation which can be controlled in a non-empirical rigorous way without requiring any additional information from the user. We also show how the search for a non-failing relaxed query over the lattice of relaxed queries can be improved by exploiting the notion of Minimal Failing Sub-queries derived from the failing query.