Fuzzy division for regular relational databases

The notion of division is very well-known in the context of regular relations and the extension of this operation to fuzzy relations is investigated in this paper. Several interpretations of the extended division can be envisaged and they depend especially on the meaning of the grades tied to the tuples of the fuzzy relations (degree of fulfilment of gradual properties, level of importance of components in a query, or uncertainty). We focus on the first two meanings which are associated with different fuzzy implications and we examine their properties and their expression in the framework of an extended SQG-like language where no specific construct for the division is available