Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE COINCIDENCE OF HYBRID HYPERIDEALS AND HYBRID INTERIOR HYPERIDEALS IN ORDERED HYPERSEMIGROUPS

  • NAREUPANAT LEKKOKSUNG (Division of Mathematics, Fuculty of Engineering, Rajamangala University of Technology Isan) ;
  • NUCHANAT TIPRACHOT (Division of Mathematics, Fuculty of Engineering, Rajamangala University of Technology Isan) ;
  • SOMSAK LEKKOKSUNG (Division of Mathematics, Fuculty of Engineering, Rajamangala University of Technology Isan)
  • Received : 2023.03.30
  • Accepted : 2023.12.31
  • Published : 2024.01.30
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Abstract

The concept of hybrid structures integrates two powerful mathematical tools: soft sets and fuzzy sets. This paper extends the application of hybrid structures to ordered hypersemigroups. We introduce the notions of hybrid interior hyperideals in ordered hypersemigroups and demonstrate their equivalence with hybrid hyperideals in certain classes, including regular, intra-regular, and semisimple ordered hypersemigroups. Furthermore, we provide a characterization of semisimple ordered hypersemigroups in terms of hybrid interior hyperideals.

Keywords

Acknowledgement

We would like to express our sincere gratitude to the anonymous referee for their valuable comments and suggestions, which significantly improved the quality of this paper.

References

  1. N. Abughazalah and N. Yaqoob, A Novel Study on Ordered Anti-Involution LA-Semihypergroups, J. Math. 2023 (2023), 6972483.
  2. M.F. Ali and N.M. Khan, Characterization of ordered semihypergroups by covered hyper-ideals, Kragujevac J. Math. 47 (2023), 417-429.
  3. T.M. Al-shami, J.C.R. Alcantud and A. Mhemdi, New generalization of fuzzy soft sets: (a, b)-fuzzy soft sets, AIMS Math. 8 (2023), 2995-3025.
  4. S. Anis, M. Khan and Y.B. Jun, Hybrid ideals in semigroups, Cogent math. 4 (2017), 1352117.
  5. T. Changphas and B. Davvaz, Properties of hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 33 (2014), 425-432.
  6. J. de Andres-Sanchez, A systematic review of the interactions of fuzzy set theory and option pricing, Expert Syst. Appl. 223 (2023), 119868.
  7. Z. Gu and X. Tang, Ordered regular equivalence relations on ordered semihypergroups, J. Algebra 450 (2016), 384-397.
  8. Z. Gu, On hyperideals of ordered semihypergroups, Ital. J. Pure Appl. Math. 40 (2018), 692-698.
  9. D. Heidari and B. Davvaz, On ordered hyperstructures, UPB Sci. Bull. A: Appl. 73 (2011), 85-96.
  10. N. Jan, J. Gwak and D. Pamucar, Mathematical analysis of generative adversarial networks based on complex picture fuzzy soft information, Appl. Soft Comput. 137 (2023), 110088.
  11. Y.B. Jun, S.Z. Song and G. Muhiuddin, Hybrid structures and applications, Ann. Commun. Math. 1 (2018), 11-25.
  12. A. Khan, M. Farooq and N. Yaqoob, Uni-soft structures applied to ordered Γ-semihypergroups, Proc. Natl. Acad. Sci. India-Phys. Sci. 90 (2020), 457-465.
  13. N. Kehayopulu and M. Tsingelis, Fuzzy interior ideals in ordered semigroups, Lobachevskii J. Mathe. 21 (2006), 65-71.
  14. N. Kehayopulu and M. Tsingelis, Fuzzy ideals in ordered semigroups, Quasigroups Related Systems 15 (2007), 279-289.
  15. N. Kehayopulu, From ordered semigroups to ordered hypersemigroups, Turk. J. Math. 42 (2018), 2045-2060.
  16. N. Kehayopulu, From ordered semigroups to ordered hypersemigroups, Turk. J. Math. 43 (2019), 21-35.
  17. J.S. Lawrence and R. Manoharan, New approach to DeMorgan's laws for soft sets via soft ideals, Appl. Nanosci. 13 (2023), 2585-2592.
  18. S. Lekkoksung, W. Samormob and K. Linesawat, On hybrid hyperideals in hypersemigroups, Proceeding of the 14th International Conference on Science, Technology and Innovation for Sustainable Well-Being (STISWB2022), Pakxe, Lao P.D.R., 2022, 144-148.
  19. J. Lu, L. Zhu and W. Gao, Remarks on bipolar cubic fuzzy graphs and its chemical applications, Int. J. Math. Comp. Eng. 1 (2023), 1-10.
  20. M. Luo and W. Li, Some new similarity measures on picture fuzzy sets and their applications, Soft Comput. 27 (2023), 6049-6067.
  21. P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (2001), 589-602.
  22. J. Mekwian and N. Lekkoksung, Hybrid ideals in ordered semigroups and some characterizations of their regularities, J. Math. Com. Sci. 11 (2021), 8075-8094.
  23. D. Molodtsov, Soft set theory first results, Comput. Math. Appl. 37 (1999), 19-31.
  24. V. Salsabeela, T.M. Athira, S.J. John and T. Baiju, Multiple criteria group decision making based on q-rung orthopair fuzzy soft sets, Granul. Comput. 8 (2023), 1067-1080.
  25. H. Sanpan, P. Kitpratyakul and S. Lekkoksung, On hybrid quasi-pure hyperideals in ordered hypersemigroups, Ann. Fuzzy Math. Inform. 25 (2023), 161-173.
  26. H. Sanpan, P. Kitpratyakul and S. Lekkoksung, On hybrid pure hyperideals in ordered hypersemigroups, Int. J. Anal. Appl. 21 (2023), 47.
  27. M. Shabir and A. Khan, Intuitionistic fuzzy interior ideals in ordered semigroups, J. Appl. Math. and Informatics 59 (2010), 539-549.
  28. J. Tang and N. Yaqoob, A novel investigation on fuzzy hyperideals in ordered *-semihypergroups, Comput. Appl. Math. 40 (2021), 43.
  29. N. Tiprachot, N. Lekkkoksung and S. Lekkoksung, On hybrid simple ordered hypersemigroups, Ann. Fuzzy Math. Inform. 26 (2023), 125-140.
  30. N. Tiprachot and B. Pibaljommee, Fuzzy interior hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 36 (2016), 859-870.
  31. M.G. Voskoglou, A Combined use of soft sets and grey numbers in decision making, J. Comp. Cog. Eng. 2 (2023), 1-4.
  32. N. Yaqoob, M. Gulistan, J. Tang and M. Azhar, On generalized fuzzy hyperideals in ordered LA-semihypergroups, Comp. Appl. Math. 38 (2019), 124.
  33. N. Yaqoob, J. Tang and J. Tang, Approximations of quasi and interior hyperfilters in partially ordered LA-semihypergroups, AIMS Mathematics 6 (2021), 7944-7960.
  34. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353.
  35. F. Zhang, W. Ma and H. Ma, Dynamic chaotic multi-attribute group decision making under weighted T-spherical fuzzy soft rough sets, Symmetry 15 (2023), 307.