The Unbounded Fuzzy Order Convergence in Fuzzy Riesz Spaces

Iqbal, Mobashir; Malik, M. G. Abbas; Bashir, Yasir; Bashir, Zia

doi:10.3390/sym11080971

Cited by 6 publications

(5 citation statements)

References 17 publications

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“…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. Moreover, this notion was redefined to unbounded fuzzy order convergence in [13]. Motivated by the previous works, we provide, in the general context of fuzzy posets, a notion of convergence for nets, in the sense of McShane [14].…”

Section: Introductionmentioning

confidence: 98%

A Notion of Convergence in Fuzzy Partially Ordered Sets

2020

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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.

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Section: Introductionmentioning

confidence: 98%

A Notion of Convergence in Fuzzy Partially Ordered Sets

2020

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“…The pair (K, τ) is called fuzzy topological vector space. For further details, we refer to [18,22,24,[31][32][33][34][35][36][37][38][39].…”

Section: Preliminariesmentioning

confidence: 99%

“…Park et al [23] defined and studied the Riesz fuzzy norm 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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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This paper aims to study fuzzy order bounded linear operators between two fuzzy Riesz spaces. Two lattice operations are defined to make the set of all bounded linear operators as a fuzzy Riesz space when the codomain is fuzzy Dedekind complete. As a special case, separation property in fuzzy order dual is studied. Furthermore, we studied fuzzy norms compatible with fuzzy ordering (fuzzy norm Riesz space) and discussed the relation between the fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.

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“…This deficiency is pointed out in Abramovich and Sirotkin (2005) for the classical order convergence. Therefore, a new definition is proposed in Iqbal et al (2019) to overcome this issue, given as follows.…”

Section: Fuzzy Order Convergencementioning

confidence: 99%

“…Park et al (2018) introduced the notion of Riesz fuzzy normed spaces. Recently, (Iqbal et al 2019) investigated the theory of unbounded fuzzy order convergence in fuzzy Riesz spaces. Like in fuzzy metric space, fuzzy norm space, and fuzzy inner product space, the completeness of fuzzy Riesz space, more precisely fuzzy Dedekind, completeness is quite important from both theoretical and application point of view, as many important theorems/results required the space to be complete to solve practical problems; for example, Banach and Schaefer's fixed point theorems are frequently used to prove the existence of solution for different types of differential equations.…”

Section: Introductionmentioning

confidence: 99%