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Archimedean components of triangular norms

Part of: Semigroups Set theory

Published online by Cambridge University Press:  09 April 2009

Erich Peter Klement ,
Radko Mesiar  and
Endre Pap
Erich Peter Klement
Affiliation:
Department of AlgebraStochastics and Knowledge-Based Mathematical SystemsJohannes Kepler UniversityA-4040 LinzAustria e-mail: ep.klement@jku.at
Radko Mesiar
Affiliation:
Department of Mathematics and Descriptive Geometry Faculty of Civil EngineeringSlovak University of TechnologySK-81 368 Bratislava Slovakia and Institute of Information Theory and Automation Czech Academy of Sciences CZ-182 08 Prague 8 Czech Republic e-mail: mesiar@math.sk
Endre Pap
Affiliation:
Department of Mathematics and InformaticsUniversity of Novi Sad, YU-21000 Novi Sad, Serbia and Montenegro e-mail: pap@im.ns.ac.yupape@eunet.yu
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Abstract

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The Archimedean components of triangular norms (which turn the closed unit interval into anabelian, 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

semigrouptriangular normArchimedean component

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 03E72: Fuzzy set theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 2 , April 2005 , pp. 239 - 255
Copyright
Copyright © Australian Mathematical Society 2005

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