A reflection on what is a membership function
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Inclou dades d'ús des de 2022
Cita com:
hdl:2099/3554
Tipus de documentArticle
Data publicació1999
EditorUniversitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
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
ISSN1134-5632
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