Triangular Norms with Continous Daigonals

Abstract

It is an old open question whether a t-norm with a continuous diagonal must be continuous [7]. We give a partial positive answer for t-norms with noncontinuous additive generators (constructed by the technique of [1, 3]). Besides this, we give necessary and sufficient conditions for a function to be the diagonal of a continuous t-norm, and we characterize all continuous t-norms with a given diagonal (according to [6]).