Abstract
In this paper, queries involving preferences are considered. Preferences are conveyed thanks to fuzzy predicates whose truth values are a matter of degree. In this framework, the result of a query is no longer a flat set of elements and each component of the answer is assigned a level of satisfaction. However, if such answers are expected to be more satisfactory from a user point of view, empty answers may still occur. The focus of the paper is put on empty answers to queries involving a division, operator which plays a central role far beyond relational database systems, especially in information retrieval systems or Web searches. In the case of an empty answer, the approach suggested here is to weaken the division and different rationales for that are proposed and discussed. It is worth mentioning that most of these weakening mechanisms are also valid for the division of regular relations.
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