Issue:Intuitionistic fuzzy group subalgebras

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Title of paper: Intuitionistic fuzzy group subalgebras Author(s): Poonam Kumar Sharma     0000-0001-5463-8665 Post-Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India pksharma@davjalandhar.com Published in: Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 2, pages 89–104 DOI: https://doi.org/10.7546/nifs.2026.32.2.89-104 Download:  PDF (272  Kb, File info) Abstract: This paper presents a systematic investigation of intuitionistic fuzzy algebraic structures associated with group algebras. We introduce the concept of an intuitionistic fuzzy group subalgebra (IFGSA) of an intuitionistic fuzzy group algebra (IFGA) constructed from the group algebra K[G], where G is a finite group and K is a field. Structural properties of IFGSAs are examined, with particular emphasis on their behavior under intuitionistic fuzzy group algebra homomorphisms (IFGA-homomorphisms). The image and inverse image of IFGSAs are studied, and it is proved that the intersection of an arbitrary family of IFGSAs is again an IFGSA. Furthermore, the notion of an intuitionistic fuzzy augmentation ideal (IFAI) in an IFGA is introduced and analyzed. It is shown that the intersection of an arbitrary family of IFAIs remains an IFAI. The image and inverse image of IFAIs under IFGA-homomorphisms are also investigated. Finally, isomorphism theorems for IFGAs are established, extending classical group algebra results to the intuitionistic fuzzy framework. Keywords: Intuitionistic fuzzy algebra, Group algebra, Intuitionistic fuzzy group subalgebra, Intuitionistic fuzzy augmentation ideal, IFGA-homomorphism. AMS Classification: 03F55, 16D10, 16W22, 22D22. References: Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. Atanassov, K. T. (1994). New operation defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 61, 137–142. Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Studies on Fuzziness and Soft Computing, Vol. 35. Physica-Verlag, Heidelberg. Basnet, D. K. (2011). Topics in Intuitionistic Fuzzy Algebra. Lambert Academic Publishing, Saarbrücken. Biswas, R. (1989). Intuitionistic fuzzy subgroup. Mathematical Forum, X, 37–46. Chiney, M., & Samanta, S. K. (2017). Intuitionistic fuzzy basis of an intuitionistic fuzzy vector space. Notes on Intuitionistic Fuzzy Sets, 23(4), 62–74. Curties, C. W., & Reiner, I. (1962). Representation Theory of Finite Groups and Associated Algebras. InterScience Publishers / John Wiley & Sons, New York. Çuvalcioğlu, G., & Aykut, E. (2015). An application of some intuitionistic fuzzy modal operators to agriculture. Notes on Intuitionistic Fuzzy Sets, 21(2), 140–149. Çuvalcioğlu, G., & Tarsuslu (Yılmaz), S. (2021). Isomorphism theorems on intuitionistic fuzzy abstract algebras. Communications in Mathematics and Applications, 12(1), 109–126. Davvaz, B., Dudek, W. A., & Jun, Y. B. (2006). Intuitionistic fuzzy Hv-submodules. Information Sciences, 176, 285–300. Elnair, M. E. (2024). More results on intuitionistic fuzzy ideals of BE-algebras. European Journal of Pure and Applied Mathematics, 17(1), 426–434. Isaac, P., & John, P. P. (2011). On intuitionistic fuzzy submodules of a module. International Journal of Mathematical Sciences and Applications, 1(3), 1447–1454. Musili, C. (1993). Representations of Finite Groups. Hindustan Book Agency, New Delhi. Rahman, S., & Saikia, H. K. (2012). Some aspects of Atanassov’s intuitionistic fuzzy submodules. International Journal of Pure and Applied Mathematics, 77(3), 369–383. Rasuli, R. (2023). Intuitionistic fuzzy G-modules with respect to norms. Notes on Intuitionistic Fuzzy Sets, 29(3), 277–291. Sharma, P. K. (2011). Intuitionistic fuzzy groups. International Journal of Data Warehousing & Mining, 1(1), 86–94. Sharma, P. K. (2013). (α,β)-Cut of intuitionistic fuzzy modules – II. Inernational Journal of Mathematical Sciences and Applications, 3(1), 11–17. Sharma, P. K. (2024). Intuitionistic fuzzy lattice ordered G-modules. Journal of Fuzzy Extension and Applications, 5(1), 141–158. Sharma, P. K. (2025). Intuitionistic fuzzy group algebra. Notes on Intuitionistic Fuzzy Sets, 31(4), 465–478. Sharma, P. K., & Kaur, T. (2015). Intuitionistic fuzzy G-modules. Notes on Intuitionistic Fuzzy Sets, 21(1), 6–23. 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. Yang, X., & Zhou, X. (2024). Ideals and homomorphism theorems of fuzzy associative algebras. Mathematics, 12(8), Article ID 1125. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338—353. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.