International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups

  • Krittika Linesawat
  • Somsak Lekkoksung*

    * Corresponding author

    Abstract

    In this paper, we introduce the notion of multi-intuitionistic fuzzy sets in ordered semigroups. The concepts of multi-intuitionistic fuzzy subsemigroups, multi-intuitionistic fuzzy left (right, two-sided, interior) ideals of an ordered semigroup are introduced and some algebraic properties of multi-intuitionistic fuzzy subsemigroups and such their multi-intuitionistic fuzzy ideals are studied. Moreover, the relationships among their multi-intuitionistic fuzzy ideals are investigated. We prove that in regular, intra-regular, and semisimple ordered semigroups, the concepts of multi-intuitionistic fuzzy interior ideals and multi-intuitionistic fuzzy ideals coincide. Finally, the new multi-intuitionistic fuzzy sets are considered.

    How to Cite

    K. Linesawat, S. Lekkoksung, A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups, Int. J. Anal. Appl. 23 (2025), 63. https://doi.org/10.28924/2291-8639-23-2025-63

    BibTeX
    @article{Linesawat2025,
  author  = {Linesawat, Krittika and Lekkoksung, Somsak},
  title   = {A Study on Multi-Intuitionistic Fuzzy Sets and Their Application in Ordered Semigroups},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {63},
  doi     = {10.28924/2291-8639-23-2025-63}
}

    References

    • [1] L.A. Zadeh, Fuzzy Sets, Inf. Control 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X.
    • [2] K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3.
    • [3] I. Cristea, B. Davvaz, Atanassov’s Intuitionistic Fuzzy Grade of Hypergroups, Inf. Sci. 180 (2010), 1506–1517. https://doi.org/10.1016/j.ins.2010.01.002.
    • [4] B. Davvaz, W. Dudek, Y. Jun, Intuitionistic Fuzzy Hv-Submodules, Inf. Sci. 176 (2006), 285–300. https://doi.org/10.1016/j.ins.2004.10.009.
    • [5] Y.B. Jun, K.H. Kim, Intuitionistic Fuzzy Ideals in BCK-Algebras, Int. J. Math. Math. Sci. 24 (2000), 839–849.
    • [6] S. Yamak, O. Kazanci, B. Davvaz, Divisible and Pure Intuitionistic Fuzzy Subgroups and Their Properties, Int. J. Fuzzy Syst. 10 (2008), 298–307.
    • [7] N. Kuroki, Fuzzy Bi-Ideals in Semigroups, Comment. Math. Univ. St. Pauli. 28 (1979), 17–21.
    • [8] N. Kehayopulu, M. Tsingelis, Fuzzy Sets in Ordered Groupoids, Semigroup Forum 65 (2002), 128–132. https://doi.org/10.1007/s002330010079.
    • [9] J. Chen, S. Li, S. Ma, X. Wang, m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets, Sci. World J. 2014 (2014), 416530. https://doi.org/10.1155/2014/416530.
    • [10] O. Kazancı, S. Hoskova-Mayerova, B. Davvaz, Multipolar Fuzzy Hyperideals in Ordered Semihypergroups, Mathematics 10 (2022), 3424. https://doi.org/10.3390/math10193424.
    • [11] N. Kehayopulu, M. Tsingelis, Fuzzy Ideals in Ordered Semigroups, Quasigroups Relat. Syst. 15 (2007), 279-289.
    • [12] N. Kehayopulu, M. Tsingelis, Fuzzy Interior Ideals in Ordered Semigroups, Lobachevskii J. Math. 21 (2006), 65-71. http://eudml.org/doc/225385.