Archimedean components of triangular norms

Erich Peter Klement, Radko Mesiar, E. Pap

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

Original languageEnglish
Pages (from-to)239-255
Number of pages17
JournalJournal of the Australian Mathematical Society
Volume78
Issue number2
Publication statusPublished - Apr 2005

Fingerprint

Triangular Norm
Additive Generator
Ordinal Sum
Ordered Semigroup
Closed
Interval
Unit

Keywords

  • Archimedean component
  • Semigroup
  • Triangular norm

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Archimedean components of triangular norms. / Klement, Erich Peter; Mesiar, Radko; Pap, E.

In: Journal of the Australian Mathematical Society, Vol. 78, No. 2, 04.2005, p. 239-255.

Research output: Contribution to journalArticle

Klement, Erich Peter ; Mesiar, Radko ; Pap, E. / Archimedean components of triangular norms. In: Journal of the Australian Mathematical Society. 2005 ; Vol. 78, No. 2. pp. 239-255.
@article{a4c15624301743bbad3de78d79bb69f9,
title = "Archimedean components of triangular norms",
abstract = "The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.",
keywords = "Archimedean component, Semigroup, Triangular norm",
author = "Klement, {Erich Peter} and Radko Mesiar and E. Pap",
year = "2005",
month = "4",
language = "English",
volume = "78",
pages = "239--255",
journal = "Journal of the Australian Mathematical Society",
issn = "1446-7887",
publisher = "Cambridge University Press",
number = "2",

}

TY - JOUR

T1 - Archimedean components of triangular norms

AU - Klement, Erich Peter

AU - Mesiar, Radko

AU - Pap, E.

PY - 2005/4

Y1 - 2005/4

N2 - The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

AB - The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed.

KW - Archimedean component

KW - Semigroup

KW - Triangular norm

UR - http://www.scopus.com/inward/record.url?scp=18944384460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18944384460&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18944384460

VL - 78

SP - 239

EP - 255

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 2

ER -