Main Article Content
Abstract
In 1982, Pawlak introduced a concept, namely the rough set theory. Several studies have been conducted regarding applying rough set theory in algebraic structures such as rough groups, rough rings, and rough modules. Furthermore, X-sub-linearly independent is a generalization of linearly independent concepts. In this paper, we investigate the X-sub-linearly independent of rough groups.
Keywords
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
- Fitriani, Surodjo, B., and Wijayanti, I. E., On X-sub-linearly independent modules, J. Phys. Conf. Ser., 893 (2017).
- Fitriani, Wijayanti, I. E., and Faisol, A., Rough X-sub-exact sequences of rough modules, Palestine Journal of Mathematics, 13(3) (2024), 773-778.
- Marsudi, Logika & Teori Himpunan, Malang : UB Press, (2010).
- Suprapto, Structure of Family of Linearly Independent Modules and Cohereditary Modules on a Category τ [M ], Dissertation Universitas Gadjah Mada, (2015).
- Nugraha, A. A., Fitriani, F., and Faisol, A., The Implementation of Rough Set on a Group Structure, Mathematics Department, Faculty of Science and Technology, UIN Sunan Ampel Surabaya, 8 (1) (2022), 45-52.
- Neelima, C. A., and Isaac, P., Rough anti-homomorphism on a rough group, Global Journal of Mathematical Science: Theory and Practical 6, 2 (2014), 79-80.
- Hafifulloh, D., Fitriani, and Faisol, A., The Properties of Rough V-Coexact Sequence in Rough Group, Barekeng: Jurnal Ilmu Matematika dan Terapan, 16 (3) (2022), 1069-1078.
- Miao, D., Han, S., Li, D., and Sun, L., Rough Group, Rough Subgroup and Their Properties, Lecture Notes in Artificial Intelligence, (2005), 105 - 113.
- Ayuni, F., Fitriani, and Faisol, A., Rough u-exact sequence of rough groups, Al-Jabar: Jurnal Pendidikan Matematika, 13 (2) (2022), 363-371.
- Dwiyanti, G., Fitriani, F., and Faisol, A., The Implementation of a Rough Set of Projective Module, Barekeng: Jurnal Ilmu Matematika dan Terapan, 17 (2) (2023), 0735-0744.
- Jesmalar, L., “Homomorphism and Isomorphism of Rough Group, Int. J. Adv. Res. Ideas Innov. Technol, 3 (3) (2017), 1382-1387.
- Setyaningsih, N., Fitriani, and Faisol, A., Sub-exact Sequence of Rough Groups, Al-Jabar: Jurnal Pendidikan Matematika, 12 (2) (2021), 267 - 272.
- Maclane, S., and Birkhoff, G., Algebra, New York: Mac Millan Publishing Co, (1979).
- Adkins, W. A. and Weintraub, S. H., Algebra: An Approach via Module Theory, New York: Springer Verlag, (1992).
- Pawlak, Z., Rough Sets, International Journal of Information and Computer Science, 11 (1982), 341-356.
References
Fitriani, Surodjo, B., and Wijayanti, I. E., On X-sub-linearly independent modules, J. Phys. Conf. Ser., 893 (2017).
Fitriani, Wijayanti, I. E., and Faisol, A., Rough X-sub-exact sequences of rough modules, Palestine Journal of Mathematics, 13(3) (2024), 773-778.
Marsudi, Logika & Teori Himpunan, Malang : UB Press, (2010).
Suprapto, Structure of Family of Linearly Independent Modules and Cohereditary Modules on a Category τ [M ], Dissertation Universitas Gadjah Mada, (2015).
Nugraha, A. A., Fitriani, F., and Faisol, A., The Implementation of Rough Set on a Group Structure, Mathematics Department, Faculty of Science and Technology, UIN Sunan Ampel Surabaya, 8 (1) (2022), 45-52.
Neelima, C. A., and Isaac, P., Rough anti-homomorphism on a rough group, Global Journal of Mathematical Science: Theory and Practical 6, 2 (2014), 79-80.
Hafifulloh, D., Fitriani, and Faisol, A., The Properties of Rough V-Coexact Sequence in Rough Group, Barekeng: Jurnal Ilmu Matematika dan Terapan, 16 (3) (2022), 1069-1078.
Miao, D., Han, S., Li, D., and Sun, L., Rough Group, Rough Subgroup and Their Properties, Lecture Notes in Artificial Intelligence, (2005), 105 - 113.
Ayuni, F., Fitriani, and Faisol, A., Rough u-exact sequence of rough groups, Al-Jabar: Jurnal Pendidikan Matematika, 13 (2) (2022), 363-371.
Dwiyanti, G., Fitriani, F., and Faisol, A., The Implementation of a Rough Set of Projective Module, Barekeng: Jurnal Ilmu Matematika dan Terapan, 17 (2) (2023), 0735-0744.
Jesmalar, L., “Homomorphism and Isomorphism of Rough Group, Int. J. Adv. Res. Ideas Innov. Technol, 3 (3) (2017), 1382-1387.
Setyaningsih, N., Fitriani, and Faisol, A., Sub-exact Sequence of Rough Groups, Al-Jabar: Jurnal Pendidikan Matematika, 12 (2) (2021), 267 - 272.
Maclane, S., and Birkhoff, G., Algebra, New York: Mac Millan Publishing Co, (1979).
Adkins, W. A. and Weintraub, S. H., Algebra: An Approach via Module Theory, New York: Springer Verlag, (1992).
Pawlak, Z., Rough Sets, International Journal of Information and Computer Science, 11 (1982), 341-356.