On internal and locally internal uninorms on bounded lattices

In this paper, we introduce the definition of an internal uninorm on an arbitrary bounded lattice L. We investigate some properties of these operators and the relationship with locally internal uninorms. We show that an internal uninorm need not always exist on an arbitrary bounded lattice. Furthermore, based on the Zermelo's well-ordering theorem, we propose two construction methods to obtain internal uninorms on a bounded lattice L with some additional constraints.