TERMINOLOGI DASAR PADA HIMPUNAN SIMETRISASI ALJABAR MIN-PLUS
Keywords: balance, min-plus algebra, symmetrization, terminology
Abstract
This paper discusses some of the terminology and basic properties of the set of min-plus algebra symmetrization. The results are algebraic structure of the positive or zero part of the set of min-plus algebra symmetrization is a semi-field, and the min-plus algebra can be viewed as the positive or zero part in the context of the set of min-plus algebra symmetrization. Furthermore, the form of the result of the subtraction of the elements in the set of min-plus algebra symmetrization, the multiplicative inverse of element in the non zero-positive and negative part, and some basic properties of balance as an analogy to the similarity of linear algebra are also obtained.
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References
Awallia, A. R., Siswanto, & Kurniawan, V. Y. (2020). Interval min-plus algebraic structure and matrices over interval min-plus algebra. Journal of Physics: Conference Series, 1494(1), 012010. https://doi.org/10.1088/1742-6596/1494/1/012010
Baccelli, F., Cohen, G., Olsder, G. J., & Quadrat, J. P. (Eds.). (2001). Synchronization and linearity: An algebra for discrete event systems. Wiley.
Darbon, J., Dower, P. M., & Meng, T. (2021). Neural network architectures using min plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs (arXiv:2105.03336). arXiv. http://arxiv.org/abs/2105.03336
De Schutter, B. (1996). Max-algebraic system theory for discrete event systems. Katholieke Universiteit Leuven.
De Schutter, B., & De Moor, B. (2002). The QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra Revisited. SIAM Review, 44(3), 417–454. https://doi.org/10.1137/S00361445024039
Goto, H. (2014). Introduction to max-plus algebra. Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC ’14, 21–22. https://doi.org/10.1145/2608628.2627496
Gyamerah, S., Boateng, P., & Harvim, P. (2016). Max-plus Algebra and Application to Matrix Operations. British Journal of Mathematics & Computer Science, 12(3), 1–14. https://doi.org/10.9734/BJMCS/2016/21639
Hook, J. (2017). Min-plus algebraic low rank matrix approximation: A new method for revealing structure in networks (arXiv:1708.06552). arXiv. http://arxiv.org/abs/1708.06552
Liebeherr, J. (2017). Opportunistic Routing in Wireless Networks. Foundations and Trends® in Networking, 11(3–4), 139–282. https://doi.org/10.1561/1300000059
Pramesthi, S. R. P. W. (2021). Simulasi Petri Net pada Proses Produksi Susu Fermentasi. VYGOTSKY, 3(1), 25. https://doi.org/10.30736/voj.v3i1.349
Putri, R. K. (2016). PENENTUAN JALUR TERPENDEK MENGGUNAKAN ALJABAR MIN-PLUS. Studi Kasus: Distribusi Kentang Jalur Pangalengan, Bandung - Jakarta. WAHANA, 66(1), 7–15. https://doi.org/10.36456/wahana.v66i1.477
Rahayu, E. W., Siswanto, S., & Wiyono, S. B. (2021). Masalah Nilai Eigen dan Eigen Mode Matriks atas Aljabar Min-Plus. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 15(4), 659–666. https://doi.org/10.30598/barekengvol15iss4pp659-666
Rosyada, S. A., Siswanto, & Kurniawan, V. Y. (2021). Bases in Min-Plus Algebra: International Conference of Mathematics and Mathematics Education (I-CMME 2021), Surakarta, Indonesia. https://doi.org/10.2991/assehr.k.211122.044
Subiono. (2015). Aljabar Min-Max Plus dan Terapannya. 173.
Suroto, S. (2022). Simetrisasi Aljabar Min-Plus. Vygotsky, 4(1), 35. https://doi.org/10.30736/voj.v4i1.444
Susilowati, E. (2018). The Comparasion Determining of Some Route of Angkot In Bandung by Using Greedy Algorithm and Min Plus Algorithm. Lontar Komputer : Jurnal Ilmiah Teknologi Informasi, 182. https://doi.org/10.24843/LKJITI.2018.v09.i03.p07
Suwanti, V., Bintoto, P., & Dinullah, R. N. I. (2017). Penerapan Min-Plus Algebra pada Penentuan Rute Tercepat Distribusi Susu. Limits: Journal of Mathematics and Its Applications, 14(2), 15. https://doi.org/10.12962/limits.v14i2.3085
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