Binary relations coming from solutions of functional equations: orderings and fuzzy subsets
Fecha
2017Autor
Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
|
10.1142/s0218488517400025
Resumen
We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equ ...
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We analyze the main properties of binary relations, defined on a nonempty set, that arise in a natural way when dealing with real-valued functions that satisfy certain classical functional equations on two variables. We also consider the converse setting, namely, given binary relations that accomplish some typical properties, we study whether or not they come from solutions of some functional equation. Applications to the numerical
representability theory of ordered structures are also furnished as a by-product. Further interpretations of this approach as well as possible generalizations to the fuzzy setting are also commented. In particular, we discuss how the values taken for bivariate functions that are bounded solutions of some classical functional equations define, in a natural way, fuzzy binary relations on a set. [--]
Materias
Functional equations on two variables,
Binary relations,
Ordered structures,
Numerical representability,
Fuzzy sets,
Fuzzy numbers,
Fuzzy relations
Editor
World Scientific Publishing Company
Publicado en
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 25, Suppl. 19 (December 2017), pp. 19-42
Notas
Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 25, Suppl. 1 (December 2017) 19-42 DOI: 10.1142/S0218488517400025 © World Scientific Publishing Company http://www.worldscientific.com/worldscinet/ijufks
Departamento
Universidad Pública de Navarra. Departamento de Automática y Computación /
Nafarroako Unibertsitate Publikoa. Automatika eta Konputazioa Saila /
Universidad Pública de Navarra. Departamento de Matemáticas /
Nafarroako Unibertsitate Publikoa. Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute of Smart Cities - ISC /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Research in Business and Economics - INARBE /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
This work has been partially supported by the research projects MTM2012-37894-C02-02, TIN2013-47605-P,
ECO2015-65031-R, MTM2015-63608-P (MINECO/FEDER), TIN2016-77356-P and the Research Services of the Public University of Navarre (Spain).
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