Fuzzy cardinality based evaluation of quantified sentences

Quantified statements are used in the resolution of a great variety of prob lems. Several methods have been proposed to evaluate statements of types I and II. The objective of this paper is to study these methods, by comparing and generalizing them. In order to do so, we propose a set of properties t hat must be fulfilled by any method of evaluation of quantified statements, we discuss some existing methods from this point of view and we describe a general approach for the evaluation of quantified statements based on the fuzzy cardinality and fuzzy relative cardinality of fuzzy sets. In addition , we discuss some concrete methods derived from the mentioned approach. The se new methods fulfill all the properties proposed and, in some cases, they provide an interpretation or generalization of existing methods. (C) 2000 Elsevier Science Inc. All rights reserved.