Equivalence relations induced by the U-partial order

In this paper, an equivalence relation on the class of uninorms with the same neutral element induced by a U-partial order is provided and discussed. The equivalence classes linked to some special uninorms are characterized. Furthermore, the set of incomparable elements with respect to the U-partial order is deeply investigated. Finally, another equivalence relation on the class of uninorms with the same neutral element is introduced and studied.