J. Aust. Math. Soc.  78 (2005), 239-255

Archimedean components of triangular norms

Erich Peter Klement   Department of Algebra   Stochastics and Knowledge-Based   Mathematical Systems   Johannes Kepler University   A-4040 Linz   Austria   ep.klement@jku.at Radko Mesiar   Department of Mathematics   and Descriptive Geometry   Faculty of Civil Engineering   Slovak University of Technology   SK-81 368 Bratislava   Slovakia   and   Institute of Information   Theory and Automation   Czech Academy of Sciences   CZ-182 08 Prague 8   Czech Republic   mesiar@math.sk and Endre Pap   Department of Mathematics   and Informatics   University of Novi Sad,   YU-21000 Novi Sad,   Serbia and Montenegro   pap@im.ns.ac.yu pape@eunet.yu

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.

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