A reflection on what is a membership function.

Trillas, Enric, and Alsina, Claudi. "A reflection on what is a membership function.." Mathware and Soft Computing 6.2-3 (1999): 201-215. <http://eudml.org/doc/39173>.

@article{Trillas1999,
abstract = {This paper is just a first approach to the idea that the membership function μP 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.},
author = {Trillas, Enric, Alsina, Claudi},
journal = {Mathware and Soft Computing},
keywords = {Lógica difusa; Función de pertenencia; Medidas difusas; membership function; partial ordering},
language = {eng},
number = {2-3},
pages = {201-215},
title = {A reflection on what is a membership function.},
url = {http://eudml.org/doc/39173},
volume = {6},
year = {1999},
}

TY - JOUR
AU - Trillas, Enric
AU - Alsina, Claudi
TI - A reflection on what is a membership function.
JO - Mathware and Soft Computing
PY - 1999
VL - 6
IS - 2-3
SP - 201
EP - 215
AB - This paper is just a first approach to the idea that the membership function μP 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.
LA - eng
KW - Lógica difusa; Función de pertenencia; Medidas difusas; membership function; partial ordering
UR - http://eudml.org/doc/39173
ER -