Novel categorical relations between $ \mathcal{L} $-fuzzy co-topologies and $ \mathcal{L} $-fuzzy ideals

Ahmed Ramadan; Anwar Fawakhreh; Enas Elkordy; Ahmed Ramadan; Anwar Fawakhreh; Enas Elkordy

doi:10.3934/math.2024999

AIMS Mathematics

2024, Volume 9, Issue 8: 20572-20587. doi: 10.3934/math.2024999

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Research article

Novel categorical relations between $ \mathcal{L} $-fuzzy co-topologies and $ \mathcal{L} $-fuzzy ideals

1.
Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni Suef, Egypt
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia; foakhrh@qu.edu.sa

Received: 25 April 2024 Revised: 31 May 2024 Accepted: 13 June 2024 Published: 25 June 2024
MSC : 03E72, 06A15, 06F07, 54A05, 54D05

The goal of this paper is to construct novel relationships among $ \mathcal{L} $-fuzzy ideal, $ \mathcal{L} $-fuzzy co-topological, and $ \mathcal{L} $-fuzzy pre-proximity spaces in complete residuated lattices. We illustrate and prove four functors between the categories of those spaces and finally, we give examples.
- complete residuated lattice,
- $ \mathcal{L} $-fuzzy ideal,
- $ \mathcal{L} $-fuzzy co-topological space,
- $ \mathcal{L} $-fuzzy pre-proximity,
- functors
Citation: Ahmed Ramadan, Anwar Fawakhreh, Enas Elkordy. Novel categorical relations between $ \mathcal{L} $-fuzzy co-topologies and $ \mathcal{L} $-fuzzy ideals[J]. AIMS Mathematics, 2024, 9(8): 20572-20587. doi: 10.3934/math.2024999

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Abstract

The goal of this paper is to construct novel relationships among $ \mathcal{L} $-fuzzy ideal, $ \mathcal{L} $-fuzzy co-topological, and $ \mathcal{L} $-fuzzy pre-proximity spaces in complete residuated lattices. We illustrate and prove four functors between the categories of those spaces and finally, we give examples.

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