Campión Arrastia, María JesúsMiguel Turullols, Laura deGarcía Catalán, Olga RaquelInduráin Eraso, EstebanAbrísqueta Usaola, Francisco Javier2018-01-092018-12-0120170218-4885 (Print)1793-6411 (Electronic)10.1142/s0218488517400025https://academica-e.unavarra.es/handle/2454/26678Electronic 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/ijufksWe 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.application/pdfeng© World Scientific Publishing CompanyFunctional equations on two variablesBinary relationsOrdered structuresNumerical representabilityFuzzy setsFuzzy numbersFuzzy relationsArtículo / ArtikuluaAcceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess