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This paper is situated in the area of imprecise (probabilistic and possibilistic) databases. Any imprecise database has a canonical interpretation as a set of more or less possible regular databases, also called worlds. In order to manipulate such databases in a safe and efficient way, a constrained framework has been previously proposed, where a restricted number of querying operations are permitted (selection, union, projection and foreign-key join which can handle attributes taking imprecise values). The key for efficiency resides in the fact that these operators do not require to make computations explicitly over all the more or less possible worlds. The division operation is dealt with in this paper and the impact of the uncertainty model on the processing technique is particularly studied.