Quantified Statements and Database Fuzzy Querying

This paper focuses on the evaluation of a particular subset of queries, namely those using fuzzy quantified predicates, which can be represented by a statement of the type “Q X are A” where Q is a fuzzy quantifier, X a set of items of the database and A a fuzzy predicate.

Abstract

Many propositions to extend database management systems have been made in the last decade. Some of them aim to support a wider range of queries involving fuzzy predicates and this paper focuses on the evaluation of a particular subset of queries, namely those using fuzzy quantified predicates. More precisely, we consider the queries which can be represented by a statement of the type "Q X are A" where Q is a fuzzy quantifier, X a set of items of the database and A a fuzzy predicate. The evaluation of this kind of statement is considered according to the propositions of Zadeh, Prade and Yager. We show that Prade and Yager's interpretation of "Q X are A", when Q is a monotonous quantifier, are respectively equivalent to a Sugeno and a Choquet fuzzy integral. Thanks to some properties of an α-cut and of fuzzy integrals, we are able to show that the evaluation of these queries, according to these three propositions, can be significantly improved with respect to a naïve strategy based on the exhaustive scan of set X.