Equivalence Classes of Uninorms

Abstract

In this paper, some properties of an order induced by uninorms are investigated. In this purpose, an equivalence relation on the class of uninorms induced by aU-partial order is investigated and discussed. Then, some properties of the set of incomparable elements with respect to the U-partial order for any uninorm on bounded lattice is investigated and the sets of incomparable elements w.r.t. U-partial order of the greatest and smallest uninorm are determined. Finally, the relationship between an order induced by uninorms and distributive property for uninorms on the unit inerval are investigated.