Relaxing the universal quantifier of the division in fuzzy relational databases

Abstract

In a previous paper, we presented an approach to calculate relational division in fuzzy databases, starting with the GEFRED model. This work centered on dealing with fuzzy attributes and fuzzy values and only the universal quantifier was taken into account since it is the inherent quantifier in classical relational division. In this paper, we present an extension of that division to relax the universal quantifier. With this new system we can use both absolute quantifiers and relative quantifiers irrespective of how the function of the fuzzy quantifier is defined. We also include a comparison with other fuzzy division approaches to relax the universal quantifier that have been published. Furthermore, in this paper we have extended the fuzzy SQL language to express any kind of fuzzy division.