An equivalence relation based on the U-partial order

Some notes on U-partial order

“…Definition 2.12. (Aşıcı F. Karaçal [1], Kesicioglu et al [14], Kesicioglu et al [13], Lu et al [17]) Let (L, ≤, 0, 1) be a bounded lattice and M be a t-norm (t-conorm, uninorm). Define the set K M as follow: [17]) Let (L, ≤, 0, 1) be a given bounded lattice.…”

“…Proposition 3.1. (Kesicioglu et al [13]) Let (L, ≤, 0, 1) be a complemented lattice and U ∈ U(e). Then, K U = L \ {0, 1}.…”

“…As an extension of t-partial order, the U-partial order U induced by uninorms, has been given in [6]. In the papers [12,13,17], some properties of U have been studied.…”

About the equivalence of nullnorms on bounded lattice

“…Recently, the order generating problem from a logical operator has been attractive for many researchers [6,8,11,12,13,14]. In this sense, in [11], a partial order called as the T-partial order induced by a t-norm has been introduced.…”

Equivalence classes of uninorms

“…10. ([20]) Let U be a nullnorm on (L, ≤, 0, 1) with neutral element e and let K L U be defined by K L U = {x ∈ L\{0, 1} | for some y ∈ L\{0, 1}, [x < y implies x U y] or [y < x implies y U x] or x y}.…”