# A reflection on what is a membership function.

Mathware and Soft Computing (1999)

- Volume: 6, Issue: 2-3, page 201-215
- ISSN: 1134-5632

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topTrillas, 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 -

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