On Archimedean triangular norms

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. (C) 1998 Elsevier Science B.V. All rights reserved.