SOFT GROUPOID AND ITS PROPERTIES

Saman Abdurrahman

Abstract


A groupoid is a generalized form of the concept of a group, achieved by omitting the properties of associativity, identity, and inverses. In this paper, we introduce the concept of a soft groupoid, which serves as a generalization of the soft group. We define and explore the properties of intersection, AND, and union on soft groupoids and soft subgroupoids. Furthermore, we explore the properties of these operations when applied to collections of soft subgroupoids derived from a given soft subgroupoid.

Keywords


Groupoid, soft groupoid, soft subgroupoid

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References


Abdurrahman, S., Arif, A. H., & Jannah, T. R. (2024). Grup Soft yang Dibangun dari Level Subset Suatu. Prosiding Seminar Nasional Lingkungan Lahan Basah. Vol. 9(3), 246–252.

https://snllb.ulm.ac.id/prosiding/index.php/snllb-lit/article/view/1065

Acar, U., Koyuncu, F., & Tanay, B. (2010). Soft Sets and Soft Rings. Computers & Mathematics with Applications. Vol. 59(11), 3458–3463.

https://doi.org/10.1016/j.camwa.2010.03.034

Aktaş, H., & Çağman, N. (2007). Soft Sets and Soft Groups. Information Sciences. Vol. 177(13), 2726–2735.

https://doi.org/10.1016/j.ins.2006.12.008

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

https://doi.org/10.3390/sym15071450

Barzegar, R., Hosseini, S. B., & Çağman, N. (2023). Second Type Nilpotent Soft Subgroups. Afrika Matematika. Vol. 34(1), 1–16.

https://doi.org/10.1007/s13370-023-01045-9

Çağman, N., Çıtak, F., & Aktaş, H. (2012). Soft Int-group and Its Applications to Group Theory. Neural Computing and Applications. Vol. 21(S1), 151–158.

https://doi.org/10.1007/s00521-011-0752-x

Çelik, Y., Ekiz, C., & Yamak, S. (2011). A new view on soft rings. Hacettepe Journal of Mathematics and Statistics. Vol. 40(2), 273–286.

Feng, F., Jun, Y. B., & Zhao, X. (2008). Soft Semirings. Computers & Mathematics with Applications. Vol. 56(10), 2621–2628.

https://doi.org/10.1016/j.camwa.2008.05.011

Ghosh, J., Mandal, D., & Samanta, T. K. (2016). Soft Group Based on Soft Element. Jordan Journal of Mathematics and Statistics. Vol. 9(2), 141–159.

Kandasamy, W. B. V. (2003). Groupoids and Smarandache Groupoids.

http://arxiv.org/abs/math/0304490

Kaygisiz, K. (2012). On soft int-groups. Annals of Fuzzy Mathematics and Informatics. Vol. 4(2), 365–375.

http://www.afmi.or.kr/papers/2012/Vol-04_No-02/PDF/AFMI-4-2(365-375)-J-111129R1.pdf

Oguz, G., Icen, I. ve Gürsoy, M. H. (2020). A New Concept in The Soft Theory: Soft Groupoids. Southeast Asian Bulletin of Mathematics. Vol. 44(4), 555–565.

Oguz, G. (2023). A Topological Approach to Soft Groupoids. Boletim Da Sociedade Paranaense de Matematica. Vol. 41(41), 1–7.

https://doi.org/10.5269/bspm.51392

Voigt, H.-M. (2022). Near Soft Groupoid. Ikonion Journal of Mathematics. Vol. 2(2), 11–16.

https://doi.org/10.1515/9783112568620-002

Yin, X., & Liao, Z. (2013). Study on Soft Groups. Journal of Computers. Vol. 8(4), 960–967.

https://doi.org/10.4304/jcp.8.4.960-967




DOI: https://doi.org/10.20527/epsilon.v18i2.13781

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