A note on moderate growth of t-conorms (Q5951751)

Given a t-conorm \(S\) on [0,1], \(S\) is said to exhibit moderate growth if for all \( a> b \) we have NEWLINE\[NEWLINE S(v,a) - S(v,b) \geq S(u,a) - S(u,v), \tag{1}NEWLINE\]NEWLINE whenever \( u > v \). Using results of C. Kimberling, R. Moynihan and A. Sklar, the author explains the relation between moderate growth an copulas, i.e., \(S\) is continuous and satisfies (1) if and only if \(S\) is an ordinal sum of continuous Archimedean t-conorms with convex additive generators.