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On Archimedean triangular norms

✍ Scribed by Sándor Jenei

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 465 KB
Volume: 99
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(97)00021-3

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✦ Synopsis

The behaviour of the additive generator functions related to a sequence of convergent continuous Archimedean triangular norm (where the limit triangular norm is continuous Archimedean) is examined in this paper. It is proved that the related generator functions converge to the generator function of the limit triangular norm in some sense under the assumption that the limit triangular norm is strict. A bit weaker convergence is proved if the limit triangular norm has 0-divisor. An example is given for the fact that the stronger type of convergence cannot be obtained in the '0-divisor limit' case.

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