Volume 2 , Issue 1 , PP: 14-20, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Mikail Bal 1 * , Katy D. Ahmad 2 , Arwa A. Hajjari 3 , Rozina Ali 4
Doi: https://doi.org/10.54216/JNFS.020102
This paper defines the concept of kernel subgroup of an intuitionistic fuzzy group. Also, it proves that this kernel is a group in the ordinary algebraic meaning as a direct application of the concept of kernel in fuzzy and anti-fuzzy groups. Also, we derive some properties of intuitionistic fuzzy groups.
intuitionistic fuzzy group, intuitionistic fuzzy kernel, fuzzy subgroup
[1] Zadeh, L., " Fuzzy Sets", Inform. Control, Vol. 8, 1965.
[2] A. ROSENFELD, Fuzzy groups, J. Math. Anal. Appl. 35 ( 1971), 512-517.
[3] P. SIVARAMAKRISHNA DAS, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84
(1981), 264-269.
[4] T. M. ANTHONY AND H. SHERWOOD, A characterizationo f fuzzy subgroups, F uzzy Sels and
Systems 7 (1982), 297-305.
[5] W. M.Wu, “Normal fuzzy subgroups,” Fuzzy Mathematics, vol.
1, no. 1, pp. 21–30, 1981.
[6] P. Bhattacharya and N.P Mukherjee, “ Fuzzy groups: Some group
theoretical and analogues, “ Inform Sci. 39 (1986),247-268
[7] D.S. Malik, J.N Mordeson and P.S. Nair, “Fuzzy Normal Subgroups in
Fuzzy groups”, J. Korean Math. Soc. 29 (1992), No. 1, pp. 1–8.
[8] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.
[9] Abobala, M., and Hatip, A., "An Algebraic Approch To Neutrosophic Euclidean Geometry", Neutrosophic Sets and Systems, Vol. 43, 2021.
[10] Palaniappan, N, Naganathan,S and Arjunan, K “ A study on Intuitionistic L-Fuzzy Subgroups”, Applied Mathematical Sciences, vol. 3 , 2009, no. 53 , 2619-2624
[11] P.K. Sharma , “( α , β ) – Cut of Intuitionistic fuzzy Groups” International
Mathematical Forum ,Vol. 6, 2011 , no. 53 , 2605-2614
[12] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic sets and systems, Vol. 45, 2021.
[13] Abobala, M., " A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences", Hindawi, 2021
[14] Abobala, M., Hatip, A., and Bal, M., " A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", International journal of neutrosophic science, Vol.17, 2021.
[15] Gupta K.c and Sarma B.K., (1999), “nilpotent fuzzy groups” ,fuzzy set and systems , vol.101, pp.167-176 .
[16] Seselja .B. and Tepavcevic A. ,(1996) , “Fuzzy groups and collections of subgroups” , fuzzy sets and systems, vol.83, pp. 85 – 91.
[18] Liu. W.J., (1982), ”Fuzzy invariant subgroups and fuzzy ideals”, fuzzy sets and systems
.vol.8. , pp.133-139 .
[19] Sankari, H, and Abobala, M, " A Contribution to m-Power Closed Groups", UMM-Alqura University Journal for Applied Sciences, KSA, 2020.
[20] Abobala, M., "On Some Neutrosophic Algebraic Equations", Journal of New Theory, Vol. 33, 2020.
[21] Abobala, M., A Study of Maximal and Minimal Ideals of n-Refined Neutrosophic Rings, Journal of Fuzzy Extension and Applications, Vol. 2, pp. 16-22, 2021.
[22] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.
[23] Malik . D. s. , Mordeson . J. N. and Nair. P. S., (1992), ” Fuzzy Generators and Fuzzy Direct
Sums of Abelian Groups”, Fuzzy sets and systems, vol.50, pp.193-199
[24] Chandrasekaran, S., and Deepica, N., "Relations between Fuzzy Subgroups and Anti-Fuzzy Subgrous" , IJRIST, Vol.5, 2019
[25] Ahmad, K., Bal, M., and Aswad, M.," The kernel of Fuzzy and Anti Fuzzy Groups",Journal of Neutrosophic and Fuzzy Systems, Vol.1, 2022.
[26] Ahmad, K., Bal, M., and Aswad, M.," A Short Note on The Solution Of Fermat's Diophantine Equation In Some Neutrosophic Rings", Journal of Neutrosophic and Fuzzy Systems, Vol. 1, 2022.
[27] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of neutrosophic science, 2022.
[28] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module Homomorphisms", International journal of neutrosophic science, 2022.
[29] Singh, P, K., Ahmad, K., Bal, M., Aswad, M.," On The Symbolic Turiyam Rings", Journal of Neutrosophic and Fuzzy Systems, 2022.
[30] Singh, P,K., " Data With Turiyam Set for Fourth Dimension Quantum Information Processing", Journal of Neutrosophic and Fuzzy Systems, vol.1, 2022.
[31] Singh, P,K., " Anti-geometry and NeutroGeometry Characterization of Non-Euclidean Data", Journal of Neutrosophic and Fuzzy Systems, vol. 1, 2022
[32] Ahmad, K., Bal, M., Hajjari, A., Ali, R.," On Imperfect Duplets In Some refined Neutrosophic Rings", Journal of Neutrosophic and Fuzzy Systems, 2022.
[33] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal of New Theory, vol. 33, 2020.
[34] Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of Neutrosophic Science", Vol. 7, pp. 74-78. 2020.
[35] Sundar, J., Vadivel, A., " New operators Using Neutrosophic Open Sets", Journal Of Neutrosophic and Fuzzy Systems, 2022.
[36] Smarandache, F., and Broumi,M., "Neutro-Intelligent Set is a particular case of the refined neutrosophic set", Journal of Neutrosophic and Fuzzy Systems, Vol. 1, 2022.
[37] Prem Kumar Singh, NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns. In: Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, April 2022, Chapter 6, DOI: 10.4018/978-1-6684-3495-6, ISBN13: 9781668434956
[38] Prem Kumar Singh, AntiGeometry and NeutroGeometry Characterization of Non-Euclidean Data Sets, Journal of Neutrosophic and Fuzzy Systems, Nov 2021, Volume 1, Issue 1, pp. 24-33, ISSN: , DOI: https://doi.org/10.54216/JNFS.0101012
[39] Prem Kumar Singh, Three-way n-valued neutrosophic concept lattice at different granulation, International Journal of Machine Learning and Cybernetics, Springer, November 2018, Vol 9, Issue 11, pp. 1839-1855,
