On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras

Surat, Ananya; Pansrigern, Nidarat; Khokhamram, Amonrat; Iampan, Aiyared

doi:10.28924/2291-8639-23-2025-314

Research Article

On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras

Ananya Surat
Nidarat Pansrigern
Amonrat Khokhamram
Aiyared Iampan*

* Corresponding author

Abstract

We introduce hesitant fuzzy sets of algebraic structures in IUP-algebras, including hesitant fuzzy IUP-subalgebras, IUP-filters, IUP-ideals, and strong IUP-ideals. These notions are defined via relaxed set-theoretic and algebraic conditions suitable for hesitant fuzzy membership functions. Their mutual relationships are analyzed, showing how they extend and unify prior definitions in the UP-algebraic setting. Several examples and counterexamples are provided to illustrate essential differences between these classes and to demonstrate that each concept is a proper generalization of its classical or fuzzy counterpart. A diagram of class inclusions is also presented to visualize the structural hierarchy among these hesitant fuzzy sets.

How to Cite

A. Surat, N. Pansrigern, A. Khokhamram, A. Iampan, On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras, Int. J. Anal. Appl. 23 (2025), 314. https://doi.org/10.28924/2291-8639-23-2025-314

BibTeX

@article{Surat2025,
  author  = {Surat, Ananya and Pansrigern, Nidarat and Khokhamram, Amonrat and Iampan, Aiyared},
  title   = {On Hesitant Fuzzy Subalgebraic Systems in IUP-Algebras},
  journal = {Int. J. Anal. Appl.},
  volume  = {23},
  year    = {2025},
  pages   = {314},
  doi     = {10.28924/2291-8639-23-2025-314}
}

References

[1] S. Aldhafeeri, G. Muhiuddin, Commutative Ideals of {Bck}-Algebras Based on Uni-Hesitant Fuzzy Set Theory, Missouri J. Math. Sci. 31 (2019), 56–65.
[2] K.M. Alsager,, n-Polar Z-Hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras, Malays. J. Math. Sci. 17 (2023), 629–644. https://doi.org/10.47836/mjms.17.4.07.
[3] C. Chanmanee, W. Nakkhase, R. Prasertpong, P. Julatha, A. Iampan, Notes on External Direct Products of Dual IUP-Algebras, South East Asian J. Math. Math. Sci. 19 (2023), 13–30. https://doi.org/10.56827/seajmms.2023.1903.2.
[4] C. Chanmanee, R. Prasertpong, P. Julatha, N. Lekkoksung, A. Iampan, On External Direct Products of IUP-Algebras, Int. J. Innov. Comput. Inf. Control 19 (2023), 775–787.
[5] M. Deepika, B. Elavarasan, J.C.G. John, Hesitant Hybrid Interior Ideals in Semigroups, J. Algebra Relat. Top. 13 (2025), 15–29. https://doi.org/10.22124/jart.2024.25776.1589.
[6] X. Fu, J. Zhang, L. Wang, The Hesitant Fuzzy Ideals in Boolean Algebra, Fuzzy Syst. Math. 34 (2020), 44–56.
[7] X. Fu, J. Zhang, L. Wang, Generalized $\alpha$-Hesitant Fuzzy Subgroups, Fuzzy Syst. Math. 35 (2021), 72–79.
[8] H. Harizavi, Y. Jun, Sup-Hesitant Fuzzy Quasi-Associative Ideals of Bci-Algebras, Filomat 34 (2020), 4189–4197. https://doi.org/10.2298/fil2012189h.
[9] A. Iampan, P. Julatha, P. Khamrot, D.A. Romano, Independent UP-Algebras, J. Math. Comput. Sci. 27 (2022), 65–76. https://doi.org/10.22436/jmcs.027.01.06.
[10] C. Inthachot, K. Moonnon, M. Visutho, P. Julatha, A. Iampan, Bipolar Fuzzy Sets in IUP-Algebras: Concepts and Analysis, Trans. Fuzzy Sets Syst. 5 (2026), 39–58.
[11] M. Jiang, Some Kinds of Anti-Hesitant Fuzzy Filters in BL-Algebras, Math. Pract. Theory 51 (2021), 205–212.
[12] U. Jittburus, P. Julatha, A. Pumila, N. Chunsee, A. Iampan, et al., New Generalizations of Sup-Hesitant Fuzzy Ideals of Semigroups, Int. J. Anal. Appl. 20 (2022), 58. https://doi.org/10.28924/2291-8639-20-2022-58.
[13] Y.B. Jun, S.S. Ahn, G. Muhiuddin, Hesitant Fuzzy Soft Subalgebras and Ideals in BCK/BCI-Algebras, Sci. World J. 2014 (2014), 763929. https://doi.org/10.1155/2014/763929.
[14] Y.B. Jun, E.H. Roh, S.S. Ahn, Hesitant Fuzzy $p$-Ideals and Quasi-Associative Ideals in BCI-Algebras, Honam Math. J. 44 (2022), 148–164.
[15] Y.B. Jun, S. Song, Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras, Bull. Sect. Log. 49 (2020), 53–78. https://doi.org/10.18778/0138-0680.2020.03.
[16] J.H. Kim, J. Lee, K. Hur, Hesitant Fuzzy Sets Applied to BCK/BCI-Algebras, Ann. Fuzzy Math. Inform. 18 (2019), 209–231. https://doi.org/10.30948/afmi.2019.18.3.209.
[17] K. Kuntama, P. Krongchai, P. Prasertpong, P. Julatha, A. Iampan, Fuzzy Set Theory Applied to IUP-Algebras, J. Math. Comput. Sci. 34 (2024), 128–143. https://doi.org/10.22436/jmcs.034.02.03.
[18] C. Liu, Hesitant Fuzzy Filters in Fuzzy Implication Algebras, Fuzzy Syst. Math. 32 (2018), 29–37.
[19] J. Man, $(\lambda, \mu)$ Hesitant Fuzzy Subalgebras of Boolean Algebras, J. Phys.: Conf. Ser. 1955 (2021), 012032. https://doi.org/10.1088/1742-6596/1955/1/012032.
[20] P. Mosrijai, A. Iampan, Anti-Type of Hesitant Fuzzy Sets on UP-Algebras, Eur. J. Pure Appl. Math. 11 (2018), 976–1002. https://doi.org/10.29020/nybg.ejpam.v11i4.3335.
[21] P. Mosrijai, A. Iampan, Hesitant Fuzzy Soft Sets over UP-Algebras, Ann. Fuzzy Math. Inform. 16 (2018), 317–331. https://doi.org/10.30948/afmi.2018.16.3.317.
[22] P. Mosrijai, A. Iampan, Some Operations on Hesitant Fuzzy Soft Sets over UP-Algebras, J. Math. Comput. Sci. 20 (2019), 131–154. https://doi.org/10.22436/jmcs.020.02.06.
[23] P. Mosrijai, W. Kamti, A. Satirad, A. Iampan, Hesitant Fuzzy Sets on UP-Algebras, Konuralp J. Math. 5 (2017), 268–280.
[24] M. Phakawat, S. Akarachai, I. Aiyared, New Types of Hesitant Fuzzy Sets on UP-Algebras, Math. Moravica 22 (2018), 29–39. https://doi.org/10.5937/matmor1802029m.
[25] P. Mosrijai, A. Satirad, A. Iampan, Partial Constant Hesitant Fuzzy Sets on UP-Algebras, J. New Theory 22 (2018), 39–50.
[26] A. Satirad, W. Kamti, A. Iampan, P. Mosrijai, Level Subsets of a Hesitant Fuzzy Set on UP-Algebras, Ann. Fuzzy Math. Inform. 14 (2017), 279–302. https://doi.org/10.30948/afmi.2017.14.3.279.
[27] K. Suayngam, P. Julatha, W. Nakkhasen, A. Iampan, Structural Insights into IUP-Algebras via Intuitionistic Neutrosophic Set Theory, Eur. J. Pure Appl. Math. 18 (2025), 5857. https://doi.org/10.29020/nybg.ejpam.v18i2.5857.
[28] K. Suayngam, P. Julatha, W. Nakkhasen, R. Prasertpong, A. Iampan, Pythagorean Neutrosophic IUP-Algebras: Theoretical Foundations and Extensions, Eur. J. Pure Appl. Math. 18 (2025), 6171. https://doi.org/10.29020/nybg.ejpam.v18i3.6171.
[29] A. Aiyared, P. Julatha, R. Prasertpong, A. Iampan, Neutrosophic Sets in IUP-Algebras: A New Exploration, Int. J. Neutrosophic Sci. 25 (2025), 540–560. https://doi.org/10.54216/ijns.250343..
[30] K. Suayngam, R. Prasertpong, N. Lekkoksung, P. Julatha, A. Iampan, Fermatean Fuzzy Set Theory Applied to IUP-Algebras, Eur. J. Pure Appl. Math. 17 (2024), 3022–3042. https://doi.org/10.2139/ssrn.4898342.
[31] K. Suayngam, R. Prasertpong, W. Nakkhasen, P. Julatha, A. Iampan, Pythagorean Fuzzy Sets: A New Perspective On IUP-Algebras, Int. J. Innov. Comput. Inf. Control 21 (2025), 339–357.
[32] K. Suayngam, T. Suwanklang, P. Julatha, R. Prasertpong, A. Iampan, New Results on Intuitionistic Fuzzy Sets in IUP-Algebras, Int. J. Innov. Comput. Inf. Control 20 (2024), 1125–1141.
[33] V. Torra, Hesitant Fuzzy Sets, Int. J. Intell. Syst. 25 (2010), 529–539. https://doi.org/10.1002/int.20418.
[34] P. Yiarayong, An $(\alpha,\beta)$-Hesitant Fuzzy Set Approach to Ideal Theory in Semigroups, Bull. Sect. Log. 51 (2022), 383–409. https://doi.org/10.18778/0138-0680.2022.13.