On the extension of SQL to fuzzy bipolar conditions

The expression of user preferences into queries addressed to a relational database management system allows to obtain more appropriate answers. In this context, it is possible to consider fuzzy bipolar conditions which are made of two parts: (i) a fuzzy constraint to represent a mandatory requirement, (ii) a fuzzy wish to represent an optional requirement. Fuzzy constraints and fuzzy wishes express user preferences and are defined by fuzzy sets. This article is a first attempt to extend the relational algebra and the SQL language to bipolar fuzzy conditions.