Supermigrative semi-copulas and triangular norms

A semi-copula S:[0,1]2→[0,1]S:[0,1]2→[0,1] is called supermigrative   if it is commutative and satisfies S(αx,y)⩾S(x,αy)S(αx,y)⩾S(x,αy) for all α∈[0,1]α∈[0,1] and for all x,y∈[0,1]x,y∈[0,1] such that y⩽xy⩽x. In this paper, the class of supermigrative semi-copulas is investigated, by focusing, in particular, on the subclass of continuous triangular norms. Some interesting connections with the theory of copulas are also underlined.