Generalized Interval Valued Fuzzy Ideals Which Coincide in Ordered Semigroups

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DOI: https://doi.org/10.28924/2291-8639-23-2025-193
Published: Aug 15, 2025
Cite as:
Thiti Gaketem, Tanaphong Prommai, Generalized Interval Valued Fuzzy Ideals Which Coincide in Ordered Semigroups, Int. J. Anal. Appl., 23 (2025), 193.

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Thiti Gaketem, Tanaphong Prommai

Abstract

In this article, we give a definition of a generalized interval valued bipolar fuzzy ideal. We can find necessary and sufficient conditions for types of generalized interval valued bipolar fuzzy ideals in ordered semigroups.

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References

  1. A. Jurio, J.A. Sanz, D. Paternain, J. Fernandez, H. Bustince, Interval-Valued Fuzzy Sets for Color Image SuperResolution, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, Berlin, Heidelberg, 2011: pp. 373–382. https://doi.org/10.1007/978-3-642-25274-7_38.
  2. H. Bustince, Indicator of Inclusion Grade for Interval-Valued Fuzzy Sets. Application to Approximate Reasoning Based on Interval-Valued Fuzzy Sets, Int. J. Approx. Reason. 23 (2000), 137–209. https://doi.org/10.1016/s0888-613x(99)00045-6.
  3. V. Chinnadurai, K. Arulmozhi Characterization of Bipolar Fuzzy Ideals in Ordered Γ-Semigroups, J. Int. Math. Virtual Inst. 8 (2018), 141–156.
  4. T. Gaketem, P. Khamrot, On Some Semigroups Characterized in Terms of Bipolar Fuzzy Weakly Interior Ideals, IAENG Int. J. Appl. Math. 48 (2021), 250–256.
  5. M. Kang, J. Kang, Bipolar Fuzzy Set Theory Applied to Sub-Semigroups with Operators in Semigroups, Pure Appl. Math. 19 (2012), 23–35. https://doi.org/10.7468/jksmeb.2012.19.1.23.
  6. C.S. Kim, J.G. Kang, J.M. Kang, Ideal Theory of Semigroups Based on the Bipolar Valued Fuzzy Set Theory, Ann. Fuzzy Math. Inf. 2 (2012), 193–206.
  7. N. Kehayopulu, Characterization of Left Quasi-Regular and Semisimple Ordered Semigroups in Terms of Fuzzy Sets, Int. J. Algebra 6 (2012), 747–755.
  8. P. Khamrot, A. Iampan, T. Gaketem, Weakly Regular Ordered Semigroups Characterized in Terms of Generalized Interval Valued Bipolar Fuzzy Ideals, IAENG Int. J. Appl. Math. 54 (2024), 1553–1559.
  9. A. Khan, Y.B. Jun, M.Z. Abbas, Characterizations of Ordered Semigroups in Terms of (ε, ε,∨q)-Fuzzy Interior Ideals, Neural Comput. Appl. 21 (2010), 433–440. https://doi.org/10.1007/s00521-010-0463-8.
  10. N. Kuroki, Fuzzy Bi-Ideals in Semigroup, Comment. Math. Univ. St. Pauli 5 (1979), 128–132.
  11. K. Lee, Bipolar-Valued Fuzzy Sets and Their Operations, in: Proceeding International Conference on Intelligent Technologies Bangkok, Thailand, pp. 307–312, (2000).
  12. A. Narayanan, T. Manikantan, Interval-valued Fuzzy Ideals Generated by an Interval-Valued Fuzzy Subset in Semigroups, J. Appl. Math. Comput. 20 (2006), 455–464. https://doi.org/10.1007/bf02831952.
  13. H. Sanpan, N. Lekkoksung, S. Lekkoksung, On Generalized Interval Valued Bipolar Fuzzy Ideals in Ordered Semigroups, J. Math. Comput. Sci. 11 (2021), 3613–3636. https://doi.org/10.28919/jmcs/5626.
  14. L. Zadeh, Fuzzy Sets, Inf. Control. 8 (1965), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x.
  15. L. Zadeh, The Concept of a Linguistic Variable and Its Application to Approximate Reasoning—I, Inf. Sci. 8 (1975), 199–249. https://doi.org/10.1016/0020-0255(75)90036-5.
  16. W. 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. The Industrial Fuzzy Control and Intelligent Systems Conference, and the NASA Joint Technology Wo, IEEE, pp. 305-309. https://doi.org/10.1109/ijcf.1994.375115.
  17. M. Zulqarnain, M. Saeed, A New Decision Making Method on Interval Valued Fuzzy Soft Matrix (IVFSM), Br. J. Math. Comput. Sci. 20 (2017), 1–17. https://doi.org/10.9734/bjmcs/2017/31243.