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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science
Full Length Article

Volume 25 • Issue 4 • PP: 80-100 • 2025

Ideals and filters on intuitionistic fuzzy lattices

Abdelhamid Bennoui 1*
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,
Soheyb Milles 1
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,
Lemnaouar Zedam 2
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1Department of Mathematics, University Center of Barika, Amdoukal Road, Barika, 05001, Algeria
2University of M’sila, University Pole, Road Bourdj Bou Arreiridj, M’sila 28000, Algeria; KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Belgium
* Corresponding Author.
DOI https://doi.org/10.54216/IJNS.250408
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Received: July 05, 2024 Revised: October 23, 2024 Accepted: December 20, 2024
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Abstract

Based on the concept of Atanassov’s intuitionistic fuzzy set on a universe X, we introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy filters on an intuitionistic fuzzy lattice. More specifically, we provide characterizations of these concepts in terms of the intuitionistic fuzzy lattice meet and join operations, in terms of some associated fuzzy sets, as well as, in terms of their crisp level sets. Furthermore, we introduce the concepts of prime intuitionistic fuzzy ideals (resp. filters) as interesting kinds, and investigate their various properties and characterizations.

Keywords

Intuitionistic fuzzy set Intuitionistic fuzzy order relation Intuitionistic fuzzy ideal Intuitionistic fuzzy filter

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format_quote
Bennoui, Abdelhamid, Milles, Soheyb, Zedam, Lemnaouar. "Ideals and filters on intuitionistic fuzzy lattices." International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, 2025, pp. 80-100. DOI: https://doi.org/10.54216/IJNS.250408
Bennoui, A., Milles, S., Zedam, L. (2025). Ideals and filters on intuitionistic fuzzy lattices. International Journal of Neutrosophic Science, Volume 25(Issue 4), 80-100. DOI: https://doi.org/10.54216/IJNS.250408
Bennoui, Abdelhamid, Milles, Soheyb, Zedam, Lemnaouar. "Ideals and filters on intuitionistic fuzzy lattices." International Journal of Neutrosophic Science Volume 25, no. Issue 4 (2025): 80-100. DOI: https://doi.org/10.54216/IJNS.250408
Bennoui, A., Milles, S., Zedam, L. (2025) 'Ideals and filters on intuitionistic fuzzy lattices', International Journal of Neutrosophic Science, Volume 25(Issue 4), pp. 80-100. DOI: https://doi.org/10.54216/IJNS.250408
Bennoui A, Milles S, Zedam L. Ideals and filters on intuitionistic fuzzy lattices. International Journal of Neutrosophic Science. 2025;Volume 25(Issue 4):80-100. DOI: https://doi.org/10.54216/IJNS.250408
A. Bennoui, S. Milles, L. Zedam, "Ideals and filters on intuitionistic fuzzy lattices," International Journal of Neutrosophic Science, vol. Volume 25, no. Issue 4, pp. 80-100, 2025. DOI: https://doi.org/10.54216/IJNS.250408
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