Hesitant hybrid interior ideals in semigroups

Document Type : Research Paper

Authors

Department of Mathematics, Karunya Institute of Technology and Sciences, Tamilnadu, India

Abstract

Hesitant fuzzy sets are very useful for dealing with group decision-making problems when experts have hesitation among several possible memberships for an element in a set. Recently, many researchers have used these concepts in clustering analysis and decision-making. In this article, the notions of hesitant hybrid subsemigroups and hesitant hybrid left
(resp., right) ideals in a semigroup are introduced, and several properties are investigated. The concept of hesitant hybrid product is also introduced, and properties of hesitant hybrid subsemigroups and hybrid left (resp., right) ideals are considered using the notion of hesitant hybrid product. Relations between hesitant hybrid intersection and hesitant hybrid product are exhibited. Additionally, we establish hesitant hybrid interior ideals in semigroups and study their
properties. Furthermore, we prove that in regular and intra-regular semigroups, the hesitant hybrid ideal and the hesitant hybrid interior ideals are coincide.

Keywords

References

[1] A. Ali, M. Khan and F. Shi, Hesitant fuzzy ideals in Abel-Grassmann’s groupoid, Ital. J. Pure Appl. Math., 17 (2015), 537-556.
[2] S. Anis, M. Khan and Y. B. Jun, Hybrid ideals in semigroups, Cogent Math., (1) 4 (2017), 1352117.
[3] J. Catherine Grace John, M. Deepika and B. Elavarasan, Hybrid interior ideals and hybrid bi-ideals in ternary semigroups, J. Intell. Fuzzy Syst., (6) 45 (2023), 10865-10872.
[4] M. Deepika, B. Elavarasan and J. John, Hybrid quasi-ideals and hybrid A-ideals in ternary semigroups, Songklanakarin Journal of Science and Technology, (1) 46 (2024).
[5] B. Elavarasan, G. Muhiuddin, K. Porselvi and Y.B. Jun, Hybrid generalized bi-ideals in semigroups, Int. J. Math. Comput. Sci., (3) 14 (2019), 601-612.
[6] T. E. Hall, On regular semigroups, J. algebra., (1) 24 (1973), 1-24.
[7] J. Howie, Fundamentals of semigroup theory, London Mathematical Society Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 12 (1995).
[8] Y. B. Jun , S. Z. Sang and G. Muhiuddin, Hybrid structures and applications, Annals of Communications in Mathematics, (1) 1 (2018), 11-25.
[9] Y. B. Jun, J. Lee Kyoung and S.Z. Song, Hesitant fuzzy bi-ideals in semigroups, Commun. Korean Math. Soc., (3) 30 (2015), 143-154.
[10] T. Mahmood, F. Mehmood and Q. Khan, Cubic hesitant fuzzy sets and their applications to multi criteria decision making, Int. J. Algebra., (1) 5 (2016), 19-51.
[11] T. Mahmood, U.Ur. Rehman and M. Albaity, Analysis of Γ􀀀 semigroups based on bipolar complex fuzzy sets, Comput. Appl. Math., (6) 42 (2023), 262.
[12] D. Molodtsov, Soft set theory-first results, Comput. Math. with Appl., 37 (1999), 19–31.
[13] K. Porselvi and B. Elavarasan, On hybrid interior ideals in semigroups, Probl. Anal. Issues Anal., (3) 8 (2019), 137-146.
[14] U. Ur. Rehman, T. Mahmood and M. Naeem, Bipolar complex fuzzy semigroups, AIMS Math., (2) 8 (2023), 3997-4021.
[15] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., (3) 35 (1971), 512-517.
[16] A. F. Talee, M.Y. Abbas and A. Basar, On properties of hesitant fuzzy ideals in semigroups, Ann. Commun. Math., (1) 3 (2020), 97-106.
[17] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., (6) 25 (2010), 529-539.
[18] V. Torra and Y. Narukawa, On hesitant fuzzy sets and decision, IEEE international conference on fuzzy systems, (2009), 1378-1382.
[19] X. Yang, T. Mahmood and U. Ur. Rehman, Bipolar complex fuzzy subgroups, Mathematics, (16) 10 (2022), 2822.
[20] L. A. Zadeh, Fuzzy sets, Inform Control., (3) 8 (1965), 338-353.
Journal of Algebra and Related Topics
Volume 13, Issue 1
July 2025
Pages 15-29

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