2-uninorms and pre-order induced by them

In Hliněná et al. (2014) the authors, inspired by Karaçal and Kesicioğlu (2011), introduced a pre-order induced by uninorms. This contribution is devoted to applying the type of relationship (the pre-order) to 2-uninorms and to show some properties of pre-orders (orders, in some cases) they induce. Philosophically, the paper follows the original idea of Clifford (1954).