Choquet type L-1-spaces of a vector capacity

[EN] Given a set function Lambda with values in a Banach space X, we construct an integration theory for scalar functions with respect to Lambda by using duality on Xand Choquet scalar integrals. Our construction extends the classical Bartle-Dunford-Schwartz integration for vector measures. Since just the minimal necessary conditions on Lambda are required, several L-1-spaces of integrable functions associated to Lambda appear in such a way that the integration map can be defined in them. We study the properties of these spaces and how they are related. We show that the behavior of the L-1-spaces and the integration map can be improved in the case when Xis an order continuous Banach lattice, providing new tools for (non-linear) operator theory and information sciences. (C) 2017 Elsevier B.V. All rights reserved.The first and second authors gratefully acknowledge the support of the Ministerio de Economia y Competitividad under projects MTM2015-65888-C4-1-P and MTM2016-77054-C2-1-P, respectively. The first author also acknowledges the support of the Junta de Andalucia (project FQM-7276), Spain.Delgado Garrido, O.; Sánchez Pérez, EA. (2017). Choquet type L-1-spaces of a vector capacity. Fuzzy Sets and Systems. 327:98-122. https://doi.org/10.1016/j.fss.2017.05.014S9812232

LIFE AND WORK OF DOMENICO CANDELORO: AN APPRECIATION

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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