A Notion of Convergence in Fuzzy Partially Ordered Sets

Dimitrios Georgiou,Athanasios Megaritis,Georgios Prinos

doi:10.3390/math8111958

Dimitrios Georgiou, Athanasios Megaritis + Show 1 more

Open Access

https://doi.org/10.3390/math8111958

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Journal: Mathematics	Publication Date: Nov 5, 2020
Citations: 2	License type: CC BY 4.0

Affiliation: University of Patras, University of Thessaly

Abstract

The notion of sequential convergence in fuzzy partially ordered sets, under the name oF-convergence, is well known. Our aim in this paper is to introduce and study a notion of net convergence, with respect to the fuzzy order relation, named o-convergence, which generalizes the former notion and is also closer to our sense of the classic concept of "convergence". The main result of this article is that the two notions of convergence are identical in the area of complete F-lattices.

Highlights

IntroductionIn his seminal paper [1] in 1971, introduced and studied the concept of fuzzy relation
Zadeh, in his seminal paper [1] in 1971, introduced and studied the concept of fuzzy relation.In particular, the notion of fuzzy order relation was initiated by generalizing the notions of reflexivity, antisymmetry and transitivity
The notion of fuzzy order relation was initiated by generalizing the notions of reflexivity, antisymmetry and transitivity

Summary

Introduction

In his seminal paper [1] in 1971, introduced and studied the concept of fuzzy relation. Using a notion of fuzzy order, the authors in [3] defined and studied a notion of convergence for sequences, in the sense of Birkhoff [10] which was further investigated in the context of fuzzy Riesz spaces in [11,12], where is considered as net convergence. This notion was redefined to unbounded fuzzy order convergence in [13].

Preliminaries

Coincidence of the Two Notions of Convergence

Conclusions