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 Títol: A reflection on what is a membership function Autor: Trillas i Gay, Enric ; Alsina Català, Claudi Editorial: Universitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica Tipus de document: Article Resum: This paper is just a first approach to the idea that the membership function $\mu _{P}$ of a fuzzy set labelled $P$ is, basically, a measure on the set of linguistic expressions $x$ is $P"$ for each $x$ in the corresponding universe of discourse $X.$ Estimating that the meaning of $P$ (relatively to $X)$ is nothing else than the use of $P$ on $X,$ these measures'' seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the predicate $P,$ that is a basic relationship like $x$ is less $P$ than $y".$ The paper only deals with predicates whose use is made by means of numerical characteristics, but those cases on which the characteristics (if they exist) are not of a numerical nature are not considered. By generalizing DeLuca-Termini's sharpened order some typical membership functions are studied as measures ISSN: 1134-5632 URI: http://hdl.handle.net/2099/3554 Apareix a les col·leccions: 1999, Vol. VI, Núm. 2-3 Comparteix: