In this paper, we discuss an approach for relaxing a failing query in the context of flexible querying. The approach relies on the notion of proximity which is defined in a relative way. We show how such proximity allows for transforming a given predicate into an enlarged one. The resulting predicate is semantically not far from the original one and it is obtained by a simple fuzzy arithmetic operation. We show also how the search for a non-failing relaxed query over the lattice of relaxed queries can be improved by exploiting the notions of MFSs (Minimal Failing Sub-queries) and MGQs (Maximally Generalized failing Queries) of the original query.