Some properties of weak uninorms

A weak uninorm is not only a generalization of a uninorm but also of a nullnorm. In this paper, we will show that, if a weak uninorm is λ-Archimedean, then it is an Archimedean nullnorm; and if a weak uninorm is e-Archimedean, then it is an Archimedean uninorm. Moreover, the De Morgan triples of the weak uninorms will be characterized, too.