Monotonic quantified statements and fuzzy integrals

Abstract

This paper is devoted to the interpretation of quantified statements of type "Q X are A", where Q is a fuzzy quantifier, X is a set of elements and A a fuzzy predicate. Our overall contribution is to propose a general view for the definition of fuzzy quantified statements. In the framework of this definition, a connection is then established between quantified statements and fuzzy integrals. We show that it is possible to define the truth value of a monotonic quantification of the type "Q X are A" as the value of a Sugeno or a Choquet fuzzy integral. Finally, we show that, when the quantifier is monotonic, Prade and Yager approaches to the evaluation of fuzzy quantified statements are respectively a Sugeno and a Choquet integral.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>