FLEXIBLE QUERIES IN RELATIONAL DATABASES - THE EXAMPLE OF THE DIVISION OPERATOR

Allowing for flexible queries enables database users to express prefer ences inside minimal requirements, and, if necessary, priorities insid e compound queries. In other words, clear-cat properties can be refine d by ordering the interpretations compatible with them, according to u ser's preferences. Often the representation of these preferences can b e viewed as modelling linguistic-like terms in requests. In this paper , the theoretical issues raised by the introduction of flexible querie s are studied in the case of the division operator, in the framework o f fuzzy sets and possibility theory. The notion of division is well-kn own in the context of regular relations and the extension of this oper ation to fuzzy relations (induced by the flexible queries) is investig ated. Several types of extended divisions can be envisaged, depending on the meaning of the grades attached to the tuples of the fuzzy relat ions (degree of fulfillment of gradual properties, level of importance of components in a query, or uncertainty pervading data). We focus on the first two meanings which are associated with different multiple-v alued logic implications and we examine their properties and their exp ression in the framework of an extended SQL-like language where no spe cific construct for the division is available.