On continuous triangular norms

Sándor Jenei

doi:10.1016/S0165-0114(97)00063-8

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On continuous triangular norms

1998-11-01

PRE

Sándor Jenei *

Fodor, JC

DOI：10.1016/S0165-0114(97)00063-8

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Abstract

En 中文

The problem of converging to any given continuous triangular-norm by a. sequence of continuous Archimedean triangular-norms is studied. Such a sequence is built up in a constructive way. The class of well-founded triangular-norms is introduced. It is proved that a sequence of triangular-norms converges to a given continuous triangular-norm if and only if this convergence is uniform. Finally, we prove that every continuous triangular norm is a uniform limit of continuous Archimedean triangular-norms. (C) 1998 Published by Elsevier Science B.V. All rights reserved.

Keywords:

triangular norms

Archimedean property

ordinal sum

uniform convergence

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