LOWER LEVEL SUBGRUPOID

Saman Abdurrahman, Na'imah Hijriati, Thresye Thresye, Moch Idris, Aprida Siska Lestia

Abstract


This study investigates the structure of anti-fuzzy subgroupoids within the framework of groupoids, extending the theory of fuzzy subgroups beyond traditional group-based algebraic systems. While numerous fuzzy approaches have been applied to groups and semigroups, the exploration of groupoids algebraic structures without the necessity of identity or inverse elements remains limited, particularly in the context of anti-fuzzy theory. This research addresses that gap by developing a mathematical characterization of anti-fuzzy subgroupoids and systematically analyzing their relationship with lower-level subsets. A key result demonstrates that every subgroupoid can be represented as a lower-level subset of a suitably constructed anti-fuzzy subgroupoid. Furthermore, it is shown that equality of two lower-level subsets occurs if and only if no element exists with a membership value strictly between the corresponding thresholds. Employing a deductive and axiomatic approach, this work contributes to the theoretical advancement of fuzzy structures in non-classical algebra. It offers a foundation for future applications in uncertainty-based decision systems

Keywords


groupoid, subgroupoid, lower-level subset, anti-fuzzy subgroupoid

Full Text:

PDF

References


Abdurrahman, S. (2022). Pengantar Struktur Aljabar : Teori Grup. Penerbit Kalam Emas.

Abdurrahman, S. (2024). Soft Groupoid and Its Properties. Epsilon: Journal Of Pure and Applied Mathematics, 18(2), 203–209. https://doi.org/https://doi.org/10.20527/epsilon.v18i2.13781

Ahmad, K. D., Bal, M., & Aswad, M. (2021). The kernel of fuzzy and anti-fuzzy groups. Jurnal of Neutrosophic and Fuzzy Systems, 1(1), 48–54.

Alajlan, A. I., & Alghamdi, A. M. (2023). Soft Groups and Characteristic Soft Subgroups. Symmetry, 15(7), 1–17.

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.

https://doi.org/https://doi.org/10.1016/S0165-0114(86)80034-3

Bhunia, S., Ghorai, G., & Xin, Q. (2021). On the characterization of pythagorean fuzzy subgroups. AIMS Mathematics, 6(1), 962–978. https://doi.org/10.3934/math.2021058

Chon, I. (2001). On T-fuzzy group. Kangweon-Kyungki Math. Jour, 9(2), 149–156.

Divya Mary Daise, S., Deepthi Mary Tresa, S., & Fernandez, S. (2020). The chain structure of intuitionistic level subgroups in cyclic groups of order pq. Malaya Journal of Matematik, 8(4), 1818–1823. https://doi.org/10.37193/CMI.2021.02.06

Divya Mary Daise, S., Deepthi Mary Tresa, S., & Fernandez, S. (2021). Intuitionistic level subgroups in cyclic groups of order p^n. South East Asian J. of Mathematics and Mathematical Sciences, 17(1), 125–138.

Gayen, S., Jha, S., Singh, M., & Prasad, A. (2021). On anti-fuzzy subgroup. Yugoslav Journal of Operations Research, 31(4), 539–546. https://doi.org/10.2298/YJOR200717043G

Kalaiarasi, K., Sudha, P., Kausar, N., Kousar, S., Pamucar, D., & Ide, N. A. D. (2022). The Characterization of Substructures of γ-Anti Fuzzy Subgroups with Application in Genetics. Discrete Dynamics in Nature and Society, 2022, 1–8.

https://doi.org/https://doi.org/10.1155/2022/1252885

Kandasamy, W. B. V. (2003). Groupoids and Smarandache Groupoids. http://arxiv.org/abs/math/0304490

Mishra, V. N., Kumar, T., Sharma, M. K., & Rathour, L. (2023). Pythagorean and fermatean fuzzy sub-group redefined in context of T ̃-norm and S ̃-conorm. Journal of Fuzzy Extension and Applications, 4(2), 125–135. https://doi.org/10.22105/jfea.2023.396751.1262

Oguz, G., Icen, I. ve Gürsoy, M. H. (2020). A new concept in the soft theory: soft groupoids. Southeast Asian Bulletin of Mathematics, 44(4)(August 2019), 555–565.

Onasanya, B. O., Ming, X., Feng, Y., & Zhang, W. (2022). Harmonization of some fuzzy subgroups. Italian Journal of Pure and Applied Mathematics, 48, 863–876.

Rajeswari, T. (2019). Alpha Level Subgroups of Alpha-Fuzzy Subgroup. International Journal of Mathematics Trends and Technology (IJMTT), 65(6), 155–158.

Rosenfeld, A. (1971). Fuzzy groups. Journal of Mathematical Analysis and Applications, 35(3), 512–517. https://doi.org/10.1016/0022-247X(71)90199-5

Thakur, P. S., Verma, R. K., & Tiwari, R. (2023). The intersection of fuzzy subgroups and relation. Algebra Letters, 2023(2023), 1–17. https://doi.org/10.28919/al/8282

Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8(3), 338–353. https://doi.org/https://doi.org/10.1016/S0019-9958(65)90241-X




DOI: https://doi.org/10.20527/epsilon.v19i2.15332

Refbacks

  • There are currently no refbacks.


Copyright (c) 2025 EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS)

Indexed by: 

      

 

EDITORIAL OFFICE 

           

 

 

 

Creative Commons License
All articles published in "Epsilon: Jurnal Matematika Murni dan Terapan" are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0). Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.