Fuzzy cardinality based evaluation of quantified sentences

Quanti®ed statements are used in the resolution of a great variety of problems. 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 that must be ful®lled by any method of evaluation of quanti®ed statements, we discuss some existing methods from this point of view and we describe a general approach for the evaluation of quanti®ed 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. These new methods ful®ll all the properties proposed and, in some cases, they provide an interpretation or generalization of existing methods. Ó 2000 Elsevier Science Inc. All rights reserved.