A note on the duality between continuous t-norm and t-conorm operators

De Morgan duality between a t-norm T and a t-conorm S is defined with respect to an involutive (or strong) negation N, so that S(x, y) = N(T(N(x), N(y))), and vice versa T(x,y) = N(S(N(x),N(y))). A weaker form of duality can be met when the negation operator N is only required to be a decreasing bijection such that S = N^-1 T(N x N). In this paper we address some issues about the (general) duality between continuous t-norms and t-conorms. Given such a t-norm T and such a t-conorm S, we show how to construct a negation N (possibly non-involutive) that makes T and S become N-dual.