On Tripolar Complex Fuzzy Sets and Their Application in Ordered Semigroups

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DOI: https://doi.org/10.28924/2291-8639-23-2025-139
Published: Jun 9, 2025
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Nuttapong Wattanasiripong, Nuchanat Tiprachot, Somsak Lekkoksung, On Tripolar Complex Fuzzy Sets and Their Application in Ordered Semigroups, Int. J. Anal. Appl., 23 (2025), 139.

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Nuttapong Wattanasiripong, Nuchanat Tiprachot, Somsak Lekkoksung

Abstract

The tripolar complex fuzzy set is a generalization of the tripolar fuzzy sets. In this paper, we introduce the notion of tripolar complex fuzzy sets in ordered semigroups. The concepts of tripolar complex fuzzy subsemigroups and tripolar complex fuzzy left (right, two-sided) ideals are introduced. Some algebraic properties of such tripolar complex fuzzy subsemigroups and their tripolar complex fuzzy ideals are studied. We characterize subsemigroup and left (resp., right, two-sided) ideals by using tripolar complex fuzzy subsemigroups and tripolar complex fuzzy left (resp., right, two-sided) ideals. Finally, we characterized intra-regular ordered semigroups in terms of tripolar complex fuzzy left ideals and tripolar complex fuzzy right ideals.

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References

  1. L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
  2. D. Ramot, M. Friedman, G. Langholz, A. Kandel, Complex Fuzzy Logic, IEEE Trans. Fuzzy Syst. 11 (2003), 450–461. https://doi.org/10.1109/TFUZZ.2003.814832.
  3. D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex Fuzzy Sets, IEEE Trans. Fuzzy Syst. 10 (2002), 171–186. https://doi.org/10.1109/91.995119.
  4. Y.B. Jun, X.L. Xin, Complex Fuzzy Sets with Application in BCK/BCI-Algebras, Bull. Sect. Logic 48 (2019), 173–185. https://doi.org/10.18778/0138-0680.48.3.02.
  5. R. Rasuli, Complex Fuzzy Lie Subalgebras and Complex Fuzzy Ideals Under t-Norms, J. Fuzzy Ext. Appl. 4 (2023), 173–187. https://doi.org/10.22105/jfea.2023.392755.1259.
  6. M. Balamurugan, T. Ramesh, A. Al-Masarwah, K. Alsager, A New Approach of Complex Fuzzy Ideals in BCK/BCIAlgebras, Mathematics 12 (2024), 1583. https://doi.org/10.3390/math12101583.
  7. P. Khamrot, A. Iampan, T. Gaketem, Bipolar Complex Fuzzy Interior Ideals in Semigroups, IAENG Int. J. Appl. Math. 54 (2024), 1110–1116.
  8. A. Jaber, On Complex Intuitionistic Fuzzy Lie Sub-Superalgebras, arXiv:2208.05765 [math.GM] (2022). https://doi.org/10.48550/arXiv.2208.05765.
  9. S. Shaqaqha, Complex Fuzzy Lie Algebras, Jordan J. Math. Stat. 13 (2020), 231–247.
  10. S. Shaqaqha, Isomorphism Theorems of Complex Fuzzy Γ-Rings, Missouri J. Math. Sci. 34 (2022), 196–207. https://doi.org/10.35834/2022/3402196.
  11. U.U. Rehman, T. Mahmood, M. Naeem, Bipolar Complex Fuzzy Semigroups, AIMS Math. 8 (2023), 3997–4021. https://doi.org/10.3934/math.2023200.
  12. M.M.K. Rao, B. Venkateswarlu, Tripolar Fuzzy Interior Ideals of a Γ-Semiring, Asia Pac. J. Math. 5 (2018), 192–207.
  13. N. Wattanasiripong, N. Lekkoksung, S. Lekkoksung, On Tripolar Fuzzy Interior Ideals in Ordered Semigroups, Int. J. Innov. Comput. Inf. Control 18 (2022), 1291–1304. https://doi.org/10.24507/ijicic.18.04.1291.
  14. N. Wattanasiripong, J. Mekwian, H. Sanpan, S. Lekkoksung, On Tripolar Fuzzy Pure Ideals in Ordered Semigroups, Int. J. Anal. Appl. 20 (2022), 49. https://doi.org/10.28924/2291-8639-20-2022-49.
  15. N. Wattanasiripong, N. Lekkoksung, S. Lekkoksung, on Tripolar Fuzzy Ideals in Ordered Semigroups, J. Appl. Math. Inform. 41 (2023), 133–154. https://doi.org/10.14317/JAMI.2023.133.
  16. N.Wattanasiripong, N. Lekkoksung, S. Lekkoksung, Description of Regular and Intra-Regular Ordered Semigroups by Tripolar Fuzzy Ideals, J. Math. Comput. Sci. 33 (2024), 290–297. https://doi.org/10.22436/jmcs.033.03.07.
  17. N. Kehayopulu, M. Tsingelis, Fuzzy Sets in Ordered Groupoids, Semigroup Forum 65 (2002), 128–132. https://doi.org/10.1007/s002330010079.
  18. X.Y. Xie, J. Tang, Regular Ordered Semigroups and Intra-Regular Ordered Semigroups in Terms of Fuzzy Subsets, Iran. J. Fuzzy Syst. 7 (2010), 121–140. https://doi.org/10.22111/ijfs.2010.180.