Equivalence classes of uninorms

Abstract

In this paper, some properties of an order induced by uninorms are studied. The set of incomparable elements with respect to the U-partial order for any uninorm on bounded lattices is investigated. Also, an equivalence relation on the class of uninorms induced by a U-partial order is investigated and discussed. Finally, the relationships between an order induced by uninorms and distributivity property for uninorms are investigated.

An Alternative Characterization of t-norms and t-conorms On An Appropriate Bounded Lattice

“…Definition 2 [7,27] Let (L, ≤, 0 L , 1 L ) be a bounded lattice. A triangular conorm S (t-conorm) is a binary operation on L which is commutative, associative, increasing with respect to both variables and it satisfies S(x, 0 L ) = x for all x ∈ L.…”