The connection between hyperideals and hybrid hyperideals through their level sets and characteristic functions in hypersemigroups

ผู้แต่ง

  • Jirapong Mekwien
  • Nareupanat Lekkoksung Rajamangala University of Technology Isan, Khon Kaen Campus

คำสำคัญ:

hypersemigroups, hybrid hyperideals, hyperideals, hyperalgebraic systems

บทคัดย่อ

While valuable in handling uncertainty, fuzzy and soft sets may sometimes prove inadequate for certain scenarios. By merging their respective strengths, leading to the advances of hybrid structures. These hybrid structures offer a robust framework for tackling uncertain problems effectively. In particular, they find application in studying hyperalgebraic structures, such as hypersemigroups. Traditionally, researchers have utilized hyperideals to explore the properties of hypersemigroups. However, our current study confirms this and provides a new perspective on the intricate relationship between hyperideals and hybrid hyperideals. By analyzing their level sets and characteristic functions, we clarify the connections between these two concepts and present an understanding of this field.

References

Birkhoff, G. (1948). Lattice theory, American Mathematical Society Colloquium, New York.

Marty, F. (1934). Sur une generalisation de la notion de groupe, paper presented in the 8th Congress Math. Scandinaves, Stockholm, Sweden, pp.45–49.

Davvaz, B. (2016). Semihypergroup Theory, Academic Press.

Heidari, D. (2024). Semihypergroups that every hyperproduct only contains some of the factors, Algebraic Structures and Their Applications, vol.11(1), pp.151–163.

Kazancı, O. and Davvaz, B. (2023). Multipolar fuzzy hyperideals in semihypergroups, Soft Computing, vol.27 (19), pp.13835 –13841.

Kehayopulu, N. (2023). What can lattices do for hypersemigroups?, Turkish Journal of Mathematics, vol.47(5), pp.1558–1572.

Tangtragoon, J., Jun, Y.B., Lekkok-sung, N. and Saengsura, K. (2023). A study on bi-interior hyperideals in hypersemi-groups, International Journal of Innovative Computing, Information and Control, vol.19(4), pp.991–1006.

Molodtsov, D. (1999). Soft set theory first results, Computers & Mathematics with Applications, vol.37(4-5), pp.19–31.

Zadeh, L.A. (1965). Fuzzy sets, In-formation and Control, vol.8(3), pp.338–353.

Jun, Y. B., Song, S.Z. and Muhi-uddin, G.(2018). Hybrid structures and applications, Annals of Communications in Mathematics, vol.1(1), pp.11–25.

Anis, S., Khan, M. and Jun, Y.B. (2017). Hybrid ideals in semigroups, Cogent Mathematics, vol.4(1), 1352117.

Elavarasan, B. and Jun, Y.B. (2023). On hybrid ideals and hybrid bi-ideals in semigroups, Iranian Journal of Mathematical Sciences and Informatics, vol.18(2), pp.1–10.

Mekwian, J. and Lekkoksung, N. (2021). Hybrid ideals in ordered semigroups and some characterizations of their regulari-ties, Journal of Mathematical and Computational Science, vol.11(6), pp.8075–8094.

Tiprachot, N., Lekkoksung, S., Pi-baljommee, B. and Lekkoksung, N. (2023). Hybrid n-interior ideals and hybrid (m, n) -ideals in ordered semigroups, Fuzzy Infor-mation and Engineering, vol.15(2), pp.128–148.

Mekwian, J., Lekkoksung, N. and Sanpan, H. (2022). A connection between bi-hyperideals and hybrid bi-hyperideals in hypersemigroups, The 14th International Conference on Science, Technology and Innovation for Sustainable Well-Being (STISWB 2022), Pakxe, Lao P.D.R.

Mekwian, J. and Lekkoksung, N. (2023). A connection between hybrid one-sided hyperideals and hybrid bi-hyperideals in hypersemigroups, Journal of Engineering and Innovative Research, vol.1(2), pp.19–24.

Lekkoksung, S., Iampan, I. and Lekkoksung, N. (2022). On ideal elements of partially ordered semigroups with the greatest element, International Journal of Innovative Computing, Information and Control, vol.18(6), pp.1941–1955.

Kehayopulu, N. (2015). On hyper-semigroups, Pure Mathematics and Applica-tions, vol. 25(2), pp.151–156.

Hasankhani, A. (1999). Ideals in a semihypergroup and Green’s relations, Ratio Mathematica, vol.13(1), pp.29–36.

Changphas, T. and Davvaz, B. (2015). Bi-hyperideals and quasi-hyperideals in ordered semi-hypergroups, Italian Journal of Pure and Applied Mathematics, vol. 35, pp.493–508.

Sanpan, H., Kitpratyakul, P. and Lekkoksung, S. (2023). On hybrid pure hy-perideals in ordered hypersemigroups, Inter-national Journal of Analysis and Applications, vol.21, 47.

Tiprachot, N., Lekkkoksung, N. and Lekkoksung, S. (2023). On hybrid sim-ple ordered hypersemigroups, Annals of Fuzzy Mathematics and Informatics, vol.26, pp.125–140.

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เผยแพร่แล้ว

2024-12-29

How to Cite

Mekwien, Jirapong, และ Nareupanat Lekkoksung. 2024. “The connection between hyperideals and hybrid hyperideals through their level sets and characteristic functions in hypersemigroups”. วารสารวิศวกรรมศาสตร์และการวิจัยเชิงนวัตกรรม 2 (2). Khon Kaen, Thailand:1-6. https://ph03.tci-thaijo.org/index.php/JEIRKKC/article/view/3275.