Characterization of Uninorms on Bounded Lattices and Pre-order They Induce

Dana Hliněná,Martin Kalina

doi:10.2991/ijcis.d.201118.001

Abstract

Characterization of Uninorms on Bounded Lattices and Pre-order They Induce

Highlights

In this paper we study pre-orders induced by uninorms on bounded lattices
The main idea of the authors of this paper is to show a relationship between families of uninorms and families of pre-orders they induce
We provide an overview of some families of uninorms on bounded lattices

Summary

INTRODUCTION

In this paper we study pre-orders induced by uninorms on bounded lattices. The main idea is based on that of Karaçal and Kesicioğlu [1], and follows the original idea of Clifford [2] and Mitsch [3]. The main idea of the authors of this paper is to show a relationship between families of uninorms and families of pre-orders (partial orders, in some cases) they induce (see Hliněná et al [4]). Another relation induced by uninorms, that is always a partial order (see Definition 16), was proposed by Ertuğrul et al [5]. The main intention of the authors was to get a partial order. This relation (partial order) does not suit well our purposes. The present paper is an extension of Hliněná and Kalina [6] that was presented at the EUSFLAT 2019 conference held in Prague

PRELIMINARIES

An Overview of Pre-Orders Induced by a Semigroup

Locally Internal Uninorms

Uninorms with Divisible Underlying T-Norm and T-Conorm

CONCLUSIONS

CONFLICTS OF INTEREST