Linguistic quantifiers modeled by Sugeno integrals

Since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them, linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning. This paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno's integral. This framework allows us to have some elegant logical properties of linguistic quantifiers. We compare carefully our new model of quantification and other approaches to linguistic quantifiers. A set of criteria for linguistic quantification was proposed in the previous literature. The relationship between these criteria and the results obtained in the present paper is clarified. Some simple applications of the Sugeno's integral semantics of quantifiers are presented. © 2006 Elsevier B.V. All rights reserved

Evaluation of Quantified Statements using Gradual Numbers - 64

Dr. Ludovic Liétard is currently assistant professor at the University of Rennes 1 (IUT Lannion) in France. His research mainly concerns flexible querying of relational databases using fuzzy set theory and various applications of fuzzy set theory in databases. Dr. Daniel Rocacher is currently assistant professor at the University of Rennes 1 (ENSSAT Lannion) in France. He has proposed new directions to define gradual numbers in the framework of fuzzy set theory. His current research concerns their applications in databases. Evaluation of Quantified Statements using Gradual Numbers -2 -Abstract. This paper is devoted to the evaluation of quantified statements which can be found in many applications as decision-making, expert systems or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type "Q X are A" and "Q B X are A". In this context, quantified statements are interpreted using an arithmetic on gradual numbers from ℕ f , ℤ f and ℚ f . It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches