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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
[[Category:Publications in Notes on IFS|{{PAGENAME}}]]
[[Category:Publications in 2026 year|{{PAGENAME}}]]
{{issue/title
| title = Intuitionistic fuzzy group subalgebras
| shortcut = nifs/32/2/89-104
}}
{{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/32/2|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
| file = NIFS-32-2-089-104.pdf
| format = PDF
| size = 272
| 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 = 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). [[Issue:Intuitionistic fuzzy basis of an intuitionistic fuzzy vector space|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). [[Issue:An application of some intuitionistic fuzzy modal operators to agriculture|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). [[Issue:Intuitionistic fuzzy G-modules with respect to norms (T and S)|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). [[Issue:Intuitionistic fuzzy group algebra|Intuitionistic fuzzy group algebra]]. Notes on Intuitionistic Fuzzy Sets, 31(4), 465–478.
# Sharma, P. K., & Kaur, T. (2015). [[Issue:Intuitionistic fuzzy G-modules|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 =
| see-also =
}}

← Older revision		Revision as of 12:30, 20 May 2026
Line 25:		Line 25:
	\| ams = 03F55, 16D10, 16W22, 22D22.		\| ams = 03F55, 16D10, 16W22, 22D22.
	\| references =		\| references =
	# Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.		# [[Krassimir Atanassov\|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. (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.		# Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Studies on Fuzziness and Soft Computing, Vol. 35. Physica-Verlag, Heidelberg.
Line 32:		Line 32:
	# Chiney, M., & Samanta, S. K. (2017). [[Issue:Intuitionistic fuzzy basis of an intuitionistic fuzzy vector space\|Intuitionistic fuzzy basis of an intuitionistic fuzzy vector space]]. Notes on Intuitionistic Fuzzy Sets, 23(4), 62–74.		# Chiney, M., & Samanta, S. K. (2017). [[Issue:Intuitionistic fuzzy basis of an intuitionistic fuzzy vector space\|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.		# 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). [[Issue:An application of some intuitionistic fuzzy modal operators to agriculture\|An application of some intuitionistic fuzzy modal operators to agriculture]]. Notes on Intuitionistic Fuzzy Sets, 21(2), 140–149.		# [[Gökhan Çuvalcioğlu\|Çuvalcioğlu, G.]], & [[Esra Aykut\|Aykut, E.]] (2015). [[Issue:An application of some intuitionistic fuzzy modal operators to agriculture\|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.		# 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.		# Davvaz, B., Dudek, W. A., & Jun, Y. B. (2006). Intuitionistic fuzzy Hv-submodules. Information Sciences, 176, 285–300.
Line 44:		Line 44:
	# Sharma, P. K. (2024). Intuitionistic fuzzy lattice ordered G-modules. Journal of Fuzzy Extension and Applications, 5(1), 141–158.		# Sharma, P. K. (2024). Intuitionistic fuzzy lattice ordered G-modules. Journal of Fuzzy Extension and Applications, 5(1), 141–158.
	# Sharma, P. K. (2025). [[Issue:Intuitionistic fuzzy group algebra\|Intuitionistic fuzzy group algebra]]. Notes on Intuitionistic Fuzzy Sets, 31(4), 465–478.		# Sharma, P. K. (2025). [[Issue:Intuitionistic fuzzy group algebra\|Intuitionistic fuzzy group algebra]]. Notes on Intuitionistic Fuzzy Sets, 31(4), 465–478.
	# Sharma, P. K., & Kaur, T. (2015). [[Issue:Intuitionistic fuzzy G-modules\|Intuitionistic fuzzy G-modules]]. Notes on Intuitionistic Fuzzy Sets, 21(1), 6–23.		# Sharma, P. K., & [[Tarandeep Kaur\|Kaur, T.]] (2015). [[Issue:Intuitionistic fuzzy G-modules\|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.		# 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.		# Yang, X., & Zhou, X. (2024). Ideals and homomorphism theorems of fuzzy associative algebras. Mathematics, 12(8), Article ID 1125.

Issue:Intuitionistic fuzzy group subalgebras - Revision history

Vassia Atanassova at 09:30, 20 May 2026