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 notn-uninorms, thus not uninorms or nullnorms.
We introduce a new construction—FS+-domain—and prove that the category withFS+-domains as objects and Scott continuous functions as morphisms is a Cartesian closed category. We obtain that the Plotkin powerdomainPP(L)over anFS-domainLis anFS+-domain.
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