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Allowing for flexible queries enables database users to express preferences inside elementary conditions and priorities between conditions. The division is one of the algebraic operators defined in order to query databases. It is mainly used in the framework of the relational model of data, although it makes sense in object-oriented databases as well. When flexible (fuzzy) predicates appear, this operator needs to be extended to fuzzy relations and this is done by replacing the usual implication by a fuzzy one. This paper proposes two types of meaning of the extended division and it investigates the issue of the primitivity of the extended operation. The final objective is to decide how flexible queries requiring such an operation should be written in an SQL-like query language.

On the primitivity of the division of fuzzy relations