Exceptions and resemblance: Two keys for tolerant division operators

The idea of extending usual Boolean queries with preferences has become a hot topic in the recent years. One of the advantages of this approach is to deliver discriminated answers instead of flat sets of elements. In this paper, preferences are conveyed thanks to fuzzy predicates whose truth values are a matter of degree. The focus is put on queries involving a division, operator which plays a central role far beyond relational database systems, especially in information retrieval systems or Web search engines. The regular division is not flexible at all and small variations in the data may lead to totally different results. The approach suggested here is to weaken the division and different rationales for that are proposed and discussed with a double requirement: to have a clear meaning from a user point of view and to deliver a resulting relation which is a quotient.