Ranks of additive generators (Q1038003)

In this paper, the author introduces the notion of a rank of an additive generator of a t-norm and a t-conorm. It is shown that cancellative and conditionally cancellative t-norms have only strong additive generators, i.e., with an infinite rank. Several examples and conditions for computation of ranks of additive generators are presented. The author also shows that the pseudo-inverse to the Cantor function is an additive generator with rank 2 of a t-conorm \(C\) and that for all \(m \in \mathbb B\), \(m \geqslant 2\), this t-conorm has an additive generator with rank \(m\). Several methods coming from functional equations are applied and various interesting open problems are stated.