Equivalence relations induced by 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.…”

“…(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. Define the relations ∼ and ∼ K on the class of all t-norms (t-conorms, uninorms with a neutral element e) on L: [12]) Let T 1 and T 2 be two t-norms on a bounded lattice (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.…”

The lattice structure for the partial orders induced by uninorms with the underlying t-norms (t-conorms ) TD (SD)

“…An order induced by uninorms on bounded lattices was given and was discussed by Ertugrul et al [9]. The orders induced by uninorms and its properties have been widely investigated in [7,14,16,21]. An order induced by a nullnorm on a bounded lattice was defined by Açıcı [2].…”

Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice

“…Later on, in [3,9], V and U-partial orders, respectively induced by nullnorms and uninorms were introduced and some basic properties of them DOI: 10.14736/kyb-2019-2-0295 were investigated. In [16], it was introduced an equivalence relations induced by the U-partial order.…”