New construction approaches of uninorms on bounded lattices

Abstract

This article continuous to investigate the construction approaches for uninorms on bounded lattices. We introduce some new methods to obtain uninorms with an identity e ∈ L\{0, 1} by using closure (interior) operators on a bounded lattice L. As a by-product of these methods, we present two families of idempotent uninorms on bounded lattices. Furthermore, we provide some corresponding examples to illustrate that our methods can differ for different closure (interior) operators.

A characterization of uninorms on bounded lattices via closure and interior operators

“…2 and an interior operator L, we propose a dual construction of uninorms on L. Moreover, we investigate the relationship between our methods and the ones described in [9,14,53]. We also demonstrate that the tools in the present paper are different from the approaches in [9,14,43,53].…”

“…2 and an interior operator L, we propose a dual construction of uninorms on L. Moreover, we investigate the relationship between our methods and the ones described in [9,14,53]. We also demonstrate that the tools in the present paper are different from the approaches in [9,14,43,53]. Accordingly, it is worth noting that the characterization of uninorms on bounded lattices via closure and interior operators contributes to enriching and analyzing the classes of uninorms on bounded lattices.…”

New structures for uninorms on bounded lattices

“…is a uninorm on L with e ∈ L \ {0, 1} iff x < y for all x ∈ I e and y ∈]e, 1[. Theorem 2.5 ( [7]) Let (L, ≤, 0, 1) be a bounded lattice with e ∈ L \ {0, 1}. (i) Let T e be a t-norm on [0, e], then the function U ∧ : L 2 → L defined by…”

“…Recently, because of "For general systems, where we cannot always expect real (or comparable) data, this extension of the underlying career together with its structure is significant..." [7], the researchers widely study uninorms on the bounded lattices instead of the unit interval [0, 1]. About the methods for the construction of uninorms, they mainly focus on t-norms (t-conorms) [1,[3][4][5][6]8,9,11,19,23], t-subnorms ( t-subconorms) [15,18,25], closure operators ( interior operators) [7,16,21,26] and additive generators [17].…”

A new approach to construct uninorms via uninorms on bounded lattices

“…In fact, t-norms (t-conorms) have been widely studied on bounded lattices by many authors (see, e. g., [8,12,18,21,22,23,30,34,35,38,44,45]), including the constructions of t-norms (t-conorms), especially in the construction of ordinal sums of t-norms (t-conorms). Then, uninorms have been extensively investigated on bounded lattices [7] and the constructions of uninorms are usually based on these tools, such as t-norms (t-conorms) (see, e. g., [1,4,5,6,9,10,11,13,15,19,20,32,33,47,49]), t-subnorms ( t-superconorms) (see, e. g., [29,31,49,52]), closure operators (interior operators) (see, e. g., [14,27,39,51]), additive generators [28] and uninorms (see, e. g., [16,48]).…”