On Tripolar Fuzzy Pure Ideals in Ordered Semigroups

Main Article Content

Nuttapong Wattanasiripong, Jirapong Mekwian, Hataikhan Sanpan, Somsak Lekkoksung


Tripolar fuzzy sets are a concept that deals with tripolar information. This idea is a generalization of bipolar and intuitionistic fuzzy sets. In this paper, the notions of tripolar fuzzy pure ideals in ordered semigroups are introduced, and some algebraic properties of tripolar fuzzy pure ideals are studied. We obtain some characterizations of weakly regular ordered semigroups in terms of tripolar fuzzy pure ideals. Finally, we introduce the concepts of tripolar weakly pure ideals and prove that the tripolar fuzzy ideals are tripolar weakly pure ideals if such tripolar fuzzy ideals satisfy the idempotent property.

Article Details


  1. J. Ahsan, M. Takahashi, Pure Spectrum of a Momoid With Zero, Kobe J. Math. 6 (1989), 163-182. https://cir.nii.ac.jp/crid/1571698601700142976.
  2. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87-96. https://dl.acm.org/doi/10.5555/1708507.1708520.
  3. N. Rehman, Pure Fuzzy Ideals in Ternary Semigroups, Int. J. Algebra Stat. 1 (2012), 1-7.
  4. T. Changphas, J. Sanborisoot, Pure Ideals in Ordered Semigroups, Kyungpook Math. J. 54 (2014), 123–129. https://doi.org/10.5666/KMJ.2014.54.1.123.
  5. N. Kehayopulu, M. Tsingelis, Fuzzy Sets in Ordered Groupoids, Semigroup Forum. 65 (2001), 128–132. https://doi.org/10.1007/s002330010079.
  6. K. Linesawat, N. Lekkoksung, S. Lekkoksung, Anti-Hybrid Pure Ideals in Ordered Semigroups, Int. J. Innov. Comput. Inform. Control. 18 (2022), 1275-1290. https://doi.org/10.24507/ijicic.18.04.1275.
  7. M.M.K. Rao, Tripolar Fuzzy Interior Ideals of Γ-Semigroup, Ann. Fuzzy Math. Inform. 15 (2018), 199–206. https://doi.org/10.30948/AFMI.2018.15.2.199.
  8. M. Murali Krishna Rao, B. Venkateswarlu, Tripolar Fuzzy Ideals of Γ-Semirings, Asia Pac. J. Math. 5 (2018), 192-207. https://doi.org/10.28924/APJM/5-2-192-207.
  9. M. Murali Krishna Rao, B. Venkateswarlu, Tripolar Fuzzy Interior Ideals and Tripolar Fuzzy Soft Interior Ideals Over Γ-Semirings, Facta Univ. Ser.: Math. Inform. 35 (2020), 29-42. https://doi.org/10.22190/FUMI2001029K.
  10. M. Murali Krishna Rao, Tripolar Fuzzy Interior Ideals and Tripolar Fuzzy Soft Interior Ideals Over Semigroups, Ann. Fuzzy Math. Inform. 20 (2020), 243-256. https://doi.org/10.30948/afmi.2020.20.3.243.
  11. A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 338-353.
  12. K. Siribute, J. Sanborisoot, On Pure Fuzzy Ideals in Ordered Semigroups, Int. J. Math. Computer Sci. 14 (2019), 867-877.
  13. Y. Xie, J. Liu, L. Wang, Further Studies on H∞ Filtering Design for Fuzzy System With Known or Unknown Premise Variables, IEEE Access. 7 (2019), 121975–121981. https://doi.org/10.1109/access.2019.2938797.
  14. L.A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.
  15. Wen-Ran Zhang, Bipolar Fuzzy Sets and Relations: A Computational Framework for Cognitive Modeling and Multiagent Decision Analysis, in: NAFIPS/IFIS/NASA ’94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. IEEE, San Antonio, TX, USA, 1994: pp. 305–309. https://doi.org/10.1109/IJCF.1994.375115.