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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2025 year|{{PAGENAME}}]]
{{issue/title
| title = Intuitionistic fuzzy group algebra
| shortcut = nifs/31/4/465-478
}}
{{issue/author
| author = Poonam Kumar Sharma
| institution = Post-Graduate Department of Mathematics, D. A. V. College
| address = Jalandhar, Punjab, India
| email-before-at = pksharma
| email-after-at = davjalandhar.com
| orcid = 0000-0001-5463-8665
}}
{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/31/4|Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4]], pages 465–478
| doi = https://doi.org/10.7546/nifs.2025.31.4.465-478
| file = NIFS-31-4-465-478.pdf
| format = PDF
| size = 225
| abstract = This paper introduces the concept of an intuitionistic fuzzy group algebra associated with a finite group ''G'' and an intuitionistic fuzzy group ''A'' on ''G''. We establish its structural properties, showing that it simultaneously behaves as an intuitionistic fuzzy algebra and an intuitionistic fuzzy ''G''-module. Extending author's earlier results on the semi-simplicity of intuitionistic fuzzy ''G''-modules, we explore links to complete reducibility and injectivity. Further, we study intersections, (''α'',''β'')-cuts, and homomorphic images of such algebras, and define intuitionistic fuzzy group algebra homomorphisms. Finally, we prove that the class of all intuitionistic fuzzy group algebras forms a category.
| keywords = Intuitionistic fuzzy ''G''-module, Intuitionistic fuzzy group, Intuitionistic fuzzy group algebra, Intuitionistic fuzzy group algebra homomorphism, Category.
| ams = 03F55, 16D10, 16D90, 16W22, 22D20.
| references =
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# Sharma, P. K. (2013). (α, β)-Cut of intuitionistic fuzzy modules-II. International Journal of Mathematical Sciences and Applications, 3(1), 11–17.
# Sharma, P. K. (2016). Direct sum of intuitionistic fuzzy submodules of G-modules. Asian Journal of Fuzzy and Applied Mathematics, 4(4), 36–46.
# Sharma, P. K. (2016). [[Issue:Isomorphism theorems for intuitionistic fuzzy submodules of G-modules|Isomorphism theorems for intuitionistic fuzzy submodules of G-modules]]. Notes on Intuitionistic Fuzzy Sets, 22(4), 80–88.
# Sharma, P. K. (2016). Reducibility and complete reducibility of intuitionistic fuzzy G-modules. Annals of Fuzzy Mathematics and Informatics, 11(6), 885–898.
# Sharma, P. K. (2016). Semi-simple intuitionistic fuzzy G-modules. International Journal of Pure and Applied Researches, 1(2), 101–108.
# Sharma, P. K. (2024). Intuitionistic fuzzy lattice ordered G-modules. Journal of Fuzzy Extension and Applications, 5(1), 141–158.
# Sharma, P. K., & Chopra, S. (2016). Injectivity of intuitionistic fuzzy G-modules. Annals of Fuzzy Mathematics and Informatics, 12(6), 805–823.
# Sharma, P. K., & Chopra, S. (2016). Projectivity of intuitionistic fuzzy G-modules. Advances in Fuzzy Sets and Systems, 21(3), 239–264.
# Sharma, P. K., & Kaur, G. (2016). [[Issue:Intuitionistic fuzzy superfluous submodule|Intuitionistic fuzzy superfluous submodule]]. Notes on Intuitionistic Fuzzy Sets, 22(3), 34–46.
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# Sharma, P. K., & Kaur, T. (2016). On intuitionistic fuzzy representation of intuitionistic fuzzy G-modules. Annals of Fuzzy Mathematics and Informatics, 11(4), 557–569.
# Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

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