Elsevier

Fuzzy Sets and Systems

Volume 99, Issue 2, 16 October 1998, Pages 179-186
Fuzzy Sets and Systems

On Archimedean triangular norms

https://doi.org/10.1016/S0165-0114(97)00021-3Get rights and content

Abstract

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.

References (3)

  • J. Fodor, S. Jenei, On continuous triangular norms, Fuzzy Sets and Systems, to...
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Current address: Department of Applied Maths & Computer Science, Janus Pannonius University, H-7601 Pécs, Hungary.

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