Some properties of idempotent uninorms on a special class of bounded lattices

Binary operations have many applications in fuzzy set theory. One of them is uninorms. In this paper, we study some properties of idempotent uninorms on bounded lattices. It is shown that idempotent uninorms on an arbitrary bounded lattice need not always be internal (with the extended definition of the term ”internal”). We give a sufficient condition for the bounded lattice to any idempotent uninorm be internal. In addition that it is given many properties of idempotent uninorms in this case.