Some investigations on the U-partial order induced by uninorms

In this paper, we study on the \( \preceq _U \) ${⪯}_U$ -partial order induced by uninorms. We also investigate some properties direct product of two uninorms on bounded lattices. We investigate some properties of the set of incomparable elements with respect to \( \preceq _U \) ${⪯}_U$ -partial. Then, we investigate the relation between the set of comparable elements and the distributivity property for uninorms on the unit interval [0, 1] . Finally, we define a total order induced by internal uninorms.