Simetrisasi Aljabar Min-Plus
DOI:
https://doi.org/10.30736/voj.v4i1.444Keywords:
Aljabar Min-Plus, Setimbang, Simetrisasi, NegatifAbstract
Pada makalah ini dibahas simetrasasi pada aljabar min-plus. Tujuan dari penelitian ini adalah mengonstruksi bentuk negatif dan setimbang dari setiap elemen pada aljabar min-plus. Metode penelitian mengadopsi dari cara perluasan aljabar max-plus menjadi aljabar max-plus tersimetri. Hasil penelitian adalah bentuk negatif dan setimbang dari elemen-elemen pada aljabar min-plus, yang dapat dianalogikan sebagai bentuk negatif dan nol pada aljabar konvesional. Hasil ini berpotensi dapat digunakan untuk mengatasi masalah invers penjumlahan pada aljabar min-plus.Downloads
References
Akian, M., Cohen, G., Gaubert, S., Nikoukhah, R., & Quadrat, J. P. (1990). Linear systems in (max, +) algebra. 29th IEEE Conference on Decision and Control, 151–156 vol.1. https://doi.org/10.1109/CDC.1990.203566
Baccelli, F., Cohen, G., Olsder, G. J., & Quadrat, J. P. (Eds.). (2001). Synchronization and linearity: An algebra for discrete event systems. Wiley.
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
Farhi, N. (2009). Modeling and control of elementary 2D-Traffic systems using Petri nets and minplus algebra. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly with 2009 28th Chinese Control Conference, 2292–2297.
https://doi.org/10.1109/CDC.2009.5400562
Golan, J. S. (2005). Some Recent Applications of Semiring Theory. Internasinal Conference on Algebra in Memory of Kostia Beidar Tainan March 6–12, 2005, 18.
Jamshidvand, S., Ghalandarzadeh, S., Amiraslani, A., & Olia, F. (2019). On the Maximal Solution of A Linear System over Tropical Semirings. ArXiv:1904.13169 [Math]. http://arxiv.org/abs/1904.13169
Li, M., & Zhao, W. (2012). Asymptotic Identity in Min-Plus Algebra: A Report on CPNS. Computational and Mathematical Methods in Medicine, 2012, 1–11. https://doi.org/10.1155/2012/154038
Litvinov, G. L., Maslov, V. P., Kushner, A. G., & Sergeev, S. N. (2012). Tropical and Idempotent Mathematics. 276.
Marjanovic, M. M. (2018). Extensions of the System N of Natural Numbers Assigned to Primary Teachers. OALib, 05(01), 1–13.
https://doi.org/10.4236/oalib.1104096
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
Spalding, A. (1998). Min-Plus Algebra and Graph Domination. Ph.D Dissertation, University of Colorado.
Speyer, D., & Sturmfels, B. (2004). Tropical Mathematics. ArXiv:Math/0408099. http://arxiv.org/abs/math/0408099
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
Watanabe, S., & Watanabe, Y. (2014). Minâ€Plus Algebra and Networks. RIMS Kokyuroku Bessatsu, B47, 041–054.
Zanardo, A., Breda, F., Meneghello, A., Cardano, F. M., & Zampieri, F. (2016). Tropical Mathematics. University of Padova, Italy.
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