Tolerant division queries and possibilistic database querying

This article is situated in the framework of the relational model of data and it focuses on two quite orthogonal issues, even if one may reasonably think that they can be mixed together. The first topic is concerned with non-traditional queries, called flexible or fuzzy queries. The key idea here is to introduce preferences inside queries addressed to a database thanks to fuzzy predicates. So doing, the user can express that some values are preferred to others, but also that some criteria are more important than others. This idea of preferences is especially illustrated with several extensions of the division operation. The second question tackled is about the handling and querying of possibilistic databases. Basically, a possibilistic database is similar to a regular one except that some attribute values are ill-known and represented as possibility distributions. In such a case, it turns out that the set of queries that can be posed to the database with acceptable performances is significantly reduced with respect to the usual relational algebra. However, it is shown that diverse types of queries of interest against possibilistic databases can be envisaged.