Convexity conditions on t-norms and their additive generators
Let T be an Archimedean (continuous) t-norm and alpha is an element of]0, 1/2[. Fodor and Ovchinnikov have studied a relation 2 between the inequality T(max(x - alpha, 0), min(x + alpha, 1)) less than or equal to T(x, x) and the convexity of the additive generator of T. Here we clarify this relation and answer open problems from previous studies. (C) 2004 Elsevier B.V. All rights reserved.
convexity t-norm additive generator