\input zb-basic \input zb-ioport \iteman{io-port 05672075} \itemau{Bosc, Patrick; Hadjali, Allel; Pivert, Olivier} \itemti{Incremental controlled relaxation of failing flexible queries.} \itemso{J. Intell. Inf. Syst. 33, No. 3, 261-283 (2009).} \itemab Summary: 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. \itemrv{~} \itemcc{} \itemut{flexible queries; cooperative answers; query relaxation; proximity relation; fuzzy number} \itemli{doi:10.1007/s10844-008-0071-6} \end