Extended Bipolar Intuitionistic Fuzzy Ideals Framework Through Level Sets and Its Characterization via Regular Ordered Γ-Semigroups

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DOI: https://doi.org/10.28924/2291-8639-24-2026-14
Published: Jan 12, 2026
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Omaima Alshanqiti, M. Palanikumar, Aiyared Iampan, Extended Bipolar Intuitionistic Fuzzy Ideals Framework Through Level Sets and Its Characterization via Regular Ordered Γ-Semigroups, Int. J. Anal. Appl., 24 (2026), 14.

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Omaima Alshanqiti, M. Palanikumar, Aiyared Iampan

Abstract

This paper proposes an extended framework for bipolar anti-intuitionistic fuzzy ideals within the context of ordered Γ-semigroups. We introduce and investigate the (δ, τ)-bipolar anti-intuitionistic fuzzy subsemigroups (BPAIFSS), including their associated left ideals, right ideals, ideals, and bi-ideals. These structures generalize existing fuzzy ideal notions by incorporating dual-valued membership and non-membership functions with flexible threshold control. Using level set analysis, we characterize the algebraic properties of these fuzzy ideals and establish their role in determining the regularity of ordered Γ-semigroups. Illustrative examples are provided to validate and demonstrate the applicability of the theoretical results.

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References

  1. Y.B. Jun, A. Khan, M. Shabir, Ordered Semigroups Characterized by Their $(sharp, sharp, curlyvee q)$-Fuzzy Bi-Ideals, Bull. Malays. Math. Sci. Soc. (2), 32 (2009), 391–408. http://eudml.org/doc/45573.
  2. M. Kang, J. Kang, Bipolar Fuzzy Set Theory Applied to Sub-Semigroups With Operators in Semigroups, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 19 (2012), 23–35. https://doi.org/10.7468/jksmeb.2012.19.1.23.
  3. N. Kehayopulu, M. Tsingelis, Fuzzy Sets in Ordered Groupoids, Semigroup Forum 65 (2001), 128–132. https://doi.org/10.1007/s002330010079.
  4. N. Kehayopulu, M. Tsingelis, Fuzzy Interior Ideals in Ordered Semigroups, Lobachevskii J. Math. 21 (2006), 65–71. http://eudml.org/doc/225385.
  5. N. KEHAYOPULU, M. TSINGELIS, Fuzzy Bi-Ideals in Ordered Semigroups, Inf. Sci. 171 (2005), 13–28. https://doi.org/10.1016/j.ins.2004.03.015.
  6. N. Kehayopulu, M. Tsingelis, Regular Ordered Semigroups in Terms of Fuzzy Subsets, Inf. Sci. 176 (2006), 3675–3693. https://doi.org/10.1016/j.ins.2006.02.004.
  7. N. Kehayopulu, M. Tsingelis, Characterization of Some Types of Ordered Semigroups in Terms of Fuzzy Sets, Lobachevskii J. Math. 29 (2008), 14–20. https://doi.org/10.1134/s1995080208010046.
  8. P. Khamrot, M. Siripitukdet, On Properties of Generalized Bipolar Fuzzy Semigroups, Songklanakarin J. Sci. Technol. 41 (2019), 405–413. https://doi.org/10.14456/SJST-PSU.2019.51.
  9. F.M. Khan, N.H. Sarmin, A. Khan, Some New Characterization of Ordered Semigroups in Terms of ((lambda ,theta))-Fuzzy Bi-Ideals, Int. J. Algebr. Stat. 1 (2012), 22–32. https://doi.org/10.20454/ijas.2012.376.
  10. N. Kuroki, On Fuzzy Semigroups, Inf. Sci. 53 (1991), 203–236. https://doi.org/10.1016/0020-0255(91)90037-u.
  11. S. Lekkoksung, On $Q$-Fuzzy Ideals in Ordered Semigroups, Int. J. Pure Appl. Math. 92 (2014), 369–379. https://doi.org/10.12732/ijpam.v92i3.5.
  12. J.N. Mordeson, D.S. Malik, N. Kuroki, Fuzzy Semigroups, Springer, (2003).
  13. A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl. 35 (1971), 512–517. https://doi.org/10.1016/0022-247x(71)90199-5.
  14. M.K. Sen, On $Gamma$-Semigroups, in: Proceedings of International Conference on Algebra and its Application, Decker publication, New York, (1981).
  15. W.R. Zhang, Bipolar Fuzzy Sets and Relations: A Computational Framework for Cognitive Modeling and Multiagent Decision Analysis, in: Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, IEEE, pp. 305–309, 1994. https://doi.org/10.1109/ijcf.1994.375115.