| Title of paper:
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Intuitionistic fuzzy Nakayama’s Lemma
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| Author(s):
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| S. Achik
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| Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
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| sofyanebenabdou@gmail.com
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| I. Bakhadach
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| Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
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| i.bakhadach@usms.ma
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| M. Oukessou
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| Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
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| ouk_mohamed@yahoo.fr
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| S. Melliani
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| Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco
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| s.melliani@usms.ma
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 4, pages 309–322
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| DOI:
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https://doi.org/10.7546/nifs.2024.30.4.309-322
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| Download:
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 PDF (230 Kb, File info)
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| Abstract:
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Drawing upon Atanassov's pioneering work on intuitionistic fuzzy sets [1], this paper presents the concept of intuitionistic fuzzy Nakayama's Lemma, offering a natural extension to Rajesh Kumar et al.'s fuzzy Nakayama's Lemma [8]. Additionally, we define the intuitionistic fuzzy Jacobson radical and explore the product of an intuitionistic fuzzy ideal and intuitionistic fuzzy submodule. Finally, we conclude by introducing the sum of two intuitionistic fuzzy submodules.
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| Keywords:
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Intuitionistic fuzzy ideal, Intuitionistic fuzzy submodule, Intuitionistic fuzzy Jacobson radical, Intuitionistic fuzzy Nakayama's Lemma.
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| AMS Classification:
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03F55, 05C25, 13B02.
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| References:
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- Atanassov, K., & Stoeva, S. (1983). Intuitionistic fuzzy sets. Polish Symposium on Interval and Fuzzy Mathematics, Poznan, 23–26.
- Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
- Atanassov, K. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
- Atanassova, L. (2007). On intuitionistic fuzzy versions of L. Zadeh's extension principle. Notes on Intuitionistic Fuzzy Sets, 13(3), 33–36.
- Azumaya, G. (1951). On maximally central algebras. Nagoya Mathematical Journal, 2, 119–150.
- Banerjee, B., & Basnet, D. K. (2003). Intuitionistic fuzzy subrings and ideals. Journal of Fuzzy Mathematics, 11, 139–155.
- Isaac, P., & Pearly John, P. (2011). On intuitionistic fuzzy submodules of a module. International Journal of Mathematical Sciences and Applications, 1, 1447–1454.
- Kumar, R., Bhambri S. K., & Kumar, P. (1995). Fuzzy submodules: Some analogues and deviations. Fuzzy Sets and Systems, 70(1), 125–130.
- Nakayama, T. (1951). A remark on finitely generated modules. Nagoya Mathematical Journal, 3, 139–140.
- Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338—353.
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