The existence of fuzzy Dedekind completion of Archimedean fuzzy Riesz space

Abstract

The fuzzy Riesz space is an attempt to study vector spaces with fuzzy ordering to model scenarios of more vague nature. The aim of this paper is to prove the existence of fuzzy Dedekind completion, whereas to achieve this goal, other related concepts like fuzzy order convergence, fuzzy positive operators, and their related results are also explored to enrich the theory of fuzzy Riesz spaces.

A Study on Fuzzy Order Bounded Linear Operators in Fuzzy Riesz Spaces

“…Iqbal et al [24] defined and characterized the notion of unbounded fuzzy order convergence in fuzzy Riesz spaces. Iqbal and Bashir [25] gave the notion of Dedekind completion of Archimedean fuzzy Riesz spaces. Recently, Cheng et al [26,27] modified the notion of fuzzy Riesz homomorphisms.…”