The equivalence of uninorms induced by the U-partial order

Abstract

In this paper, some properties of an order induced by uninorms are investigated. In this aim, the set of incomparable elements with respect to the U-partial order for any uninorm is introduced and studied. Also, by defining such an order, an equivalence relation on the classofuninormsisdefinedandthisequivalenceisdeeplyinvestigated. Finally,anotherset ofincomparableelementswithrespecttothe U-partialorderforanyuninormisintroduced and studied.