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Issue:On intuitionistic fuzzy characteristic and Frattini subgroups

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Title of paper: On intuitionistic fuzzy characteristic and Frattini subgroups
Author(s):
Paul Augustine Ejegwa     0000-0003-4834-6433
Department of Mathematics, Joseph Sarwuan Tarka University, Makurdi, Nigeria
ejegwa.augustine@uam.edu.ng
Ahmed Ibrahim Isah     0000-0003-0673-4016
Department of Mathematical Sciences, Kaduna State University, Kaduna, Nigeria
ahmed.isah@kasu.edu.ng
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 1, pages 64–79
DOI: https://doi.org/10.7546/nifs.2025.31.1.64-79
Download:  PDF (231  Kb, File info)
Abstract: This paper presents intuitionistic fuzzy characteristic subgroups and discusses some of its properties. It is established that an intuitionistic fuzzy subgroup of an intuitionistic fuzzy group is characteristic provided its cuts are characteristic subgroups. In addition, it is proven that every intuitionistic fuzzy characteristic subgroup of an intuitionistic fuzzy group is an intuitionistic fuzzy normal subgroup. Furthermore, the notions of intuitionistic fuzzy maximal subgroups and intuitionistic fuzzy Frattini subgroups are established. It is shown that every intuitionistic fuzzy Frattini subgroup is an intuitionistic fuzzy characteristic subgroup as well as an intuitionistic fuzzy normal subgroup, respectively. Finally, some results on intuitionistic fuzzy Frattini subgroups are presented with regards to the level sets and cuts of an intuitionistic fuzzy groups.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy groups, Intuitionistic fuzzy subgroups, Intuitionistic fuzzy normal subgroup, Intuitionistic fuzzy Frattini subgroups, Intuitionistic fuzzy characteristic subgroups.
AMS Classification: 03F55, 06D72, 08A72.
References:
  1. Ahemen, S., Ujah, R., & Ejegwa, P. A. (2024). New cosine similarity measures for intuitionistic fuzzy sets with application in decision-making. In: Ali, I., Modibbo, U.M., Bolaji, A. L., & Garg, H. (eds). Optimization and Computing using Intelligent Data-Driven Approaches for Decision-Making: Optimization Applications, 55–69. CRC Press.
  2. Ahn, T. C., Hur, K., Jang, K. W., & Roh, S. B. (2006). Intuitionistic fuzzy subgroups. Honam Mathematical Journal, 28(1), 31–44.
  3. Ahn, T. C., Jang, K. W., Roh, S. B., & Hur, K. (2005). A note on intuitionistic fuzzy subgroups. Proceedings of KFIS Autumn Conference 2005, 15(2), 496–499.
  4. Ajmal, N., & Jahan, I. (2012). A study of normal fuzzy subgroups and characteristic fuzzy subgroups of a fuzzy group. Fuzzy Information and Engineering, 4(2), 123–143.
  5. Alolaiyan, H., Shuaib, U., Latif, L., & Razaq, A. (2019). t-Intuitionistic fuzzification of Lagrange’s theorem of t-intuitionistic fuzzy subgroup. IEEE Access, 7, 158419–158426.
  6. Anthony, J. M., & Sherwood, H. (1982). A characterization of fuzzy subgroups. Fuzzy Sets and Systems, 7(3), 297–305.
  7. Anum, M. T., Zhang, H., Ejegwa, P. A., & Feng, Y. (2024). Tendency coefficient-based weighted distance measure for intuitionistic fuzzy sets with applications. Proceedings of the 12th International Conference on Intelligent Control and Information Processing (ICICIP 2024), Nanjing, China, 54–61.
  8. Atanassov, K. T. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Science-Technical Library of Bulgaria Academic of Science, 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6.
  9. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  10. Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 61(2), 137–142.
  11. Bal, M., Ahmad, K.D., Hajjari, A.A., & Ali, R. (2022). A short note on the kernel subgroup of intuitionistic fuzzy groups. Journal of Neutrosophic and Fuzzy Systems, 2(1), 14–20.
  12. Biswas, R. (1989). Intuitionistic fuzzy subgroups. Mathematical Forum, 10, 37–46.
  13. Biswas, R. (1997). Intuitionistic fuzzy subgroups. Notes on Intuitionistic Fuzzy Sets, 3(2), 53–60.
  14. Ejegwa, P. A., Ajogwu, C. F., & Sarkar, A. (2023). A hybridized correlation coefficient technique and its application in classification process under intuitionistic fuzzy setting. Iranian Journal of Fuzzy Systems, 20(4), 103–120.
  15. Ejegwa, P. A., Akowe, S. O., Otene, P. M., & Ikyule, J. M. (2014). An overview on intuitionistic fuzzy sets. International Journal of Scientific and Technological Research, 3(3), 142–145.
  16. Ejegwa, P. A., Feng, Y., & Zhang, W. (2023). Solvability in fuzzy multigroup context. Italian Journal of Pure and Applied Mathematics, 49, 713–721.
  17. Ejegwa, P. A., & Otuwe, J. A. (2019). Frattini fuzzy subgroups of fuzzy groups. Journal of Universal Mathematics, 2(2), 175–182.
  18. Fathi, M., & Salleh, A. R. (2009). Intuitionistic fuzzy groups. Asian Journal of Algebra, 2(1), 1–10.
  19. Hur, K. & Jang, S.Y. (2006). The lattice of intuitionistic fuzzy congruences, International Mathematical Forum, 1(5), 211–236.
  20. Husban, R. A., Salleh, A. R., & Ahmad, A. G. B. (2016). Complex intuitionistic fuzzy group, Global Journal of Pure and Applied Mathematics, 12(6), 4929–4949.
  21. Husban, R. A., Salleh, A. R., & Ahmad, A. G. B. (2017). Complex intuitionistic fuzzy normal subgroup, International Journal of Pure and Applied Mathematics, 115(3), 455–466.
  22. Kim, D. S. (2003). Characteristic fuzzy groups. Communications of Korean Mathematical Society, 18(1), 21–29.
  23. Kumar, R. (1992). Fuzzy characteristic subgroups of a group. Fuzzy Sets and Systems, 45, 397–398.
  24. Latif, L., Shuaib, U., Alolaiyan, H., & Razaq, A. (2018). On fundamental theorems of t-intuitionistic fuzzy isomorphism of t-intuitionistic fuzzy subgroups. IEEE Access, 6, 74547–74556.
  25. Li, D. Y., Zhang, C. Y., & Ma, S. Q. (2009). The intuitionistic anti-fuzzy subgroup in group G. In: Cao, B. Y., Zhang, C. Y., Li, T. F. (eds). Fuzzy Information and Engineering, Advances in Soft Computing, vol 54. Springer, Berlin, Heidelberg.
  26. Onoja, M. A., Anum, M. T., Ejegwa, P. A., & Isife, K. I. (2024). Weighted intuitionistic fuzzy distance metrics in solving cases of pattern recognition and disease diagnosis. Risk Assessment and Management Decisions, 1(1), 88–101.
  27. Rosenfeld, A. (1971). Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3), 512–517.
  28. Sharma, P. K. (2011). Homomorphism of intuitionistic fuzzy groups. International Mathematical Forum, 6(64), 3169–3178.
  29. Sharma, P. K. (2011). Intuitionistic fuzzy groups. International Journal of Data Warehousing and Mining, 1(1), 86–94.
  30. Sharma, P. K. (2011). (α, β)-Cut of intuitionistic fuzzy groups. International Mathematical Forum, 6(53), 2605–2614.
  31. Sharma, P. K. (2012). On the direct product of intuitionistic fuzzy subgroups. International Mathematical Forum, 7, 2(11), 523–530.
  32. Sharma, P. K. (2012). t-Intuitionistic fuzzy subgroups. International Journal of Fuzzy Mathematics and Systems, 2(3), 233–243.
  33. Xu, C. (2008). New structures of intuitionistic fuzzy groups. In: Huang, D. S., Wunsch, D. C., Levine D. S., & Jo, K. H. (eds). Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. Communications in Computer and Information Science, vol 15. Springer, Berlin, Heidelberg, 145–152.
  34. Yuan, X. H., Li, H. X., Lee, E. S. (2010). On the definition of the intuitionistic fuzzy subgroups. Computers and Mathematics with Applications, 59(9), 3117–3129.
  35. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
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