Convexity conditions on t-norms and their additive generators

Let T be an Archimedean (continuous) t-norm and α∈]0,12[. Fodor and Ovchinnikov have studied a relation between the inequality T(max(x-α,0),min(x+α,1))⩽T(x,x) and the convexity of the additive generator of T. Here we clarify this relation and answer open problems from previous studies.