Ranks of additive generators

For additive generators of t-norms and t-conorms, the concept of a rank is introduced. It is shown that cancellative and conditionally cancellative t-norms have only additive generators with an infinite rank. The conditions for additive generators with finite ranks are introduced and several examples are given. It is shown 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∈N, m⩾2 this t-conorm has an additive generator with rank m.