It is proved that, except for the uninorms and the nullnorms, there are no continuous weak uninorms who have no more than one nontrivial idempotent element. And some examples of discontinuous weak uninorms are shown. All of these examples are not -uninorms, thus not uninorms or nullnorms.
"Some Examples of Weak Uninorms." Abstr. Appl. Anal. 2013 1 - 5, 2013. https://doi.org/10.1155/2013/712690