PERMANENT AND DOMINANT OF MATRIX OVER INTERVAL MIN-PLUS ALGEBRA

  • Ade Safira Septiany Pure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0009-0009-6325-1134
  • Siswanto Siswanto Pure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0001-8168-734X
  • Vika Yugi Kurniawan Pure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0001-8475-7243
DOI: https://doi.org/10.30598/barekengvol18iss3pp2029-2034
Keywords: Permanent, Dominant, Matrix, Interval Min-Plus Algebra

Abstract

A min-plus algebra is a set , where  is the set of all real numbers equipped with two binary operations, namely minimum  and addition . Every square matrix in min-plus algebra can always be calculated as a permanent and dominant matrix. The min-plus algebra can be extended to an interval min-plus algebra, where the elements are closed intervals denoted  with two binary operations, minimum  and addition . Min-plus interval algebra can be defined in a square matrix. This research will discuss the permanent and dominant a matrix over min-plus interval algebra, the relationship between permanent and dominant matrix, and bideterminant matrix over min-plus interval algebra. From the research results obtained, permanent and dominant formulas, it found that the dominant is greater than or equal to the permanent and the bideterminant formulas.

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References

Y. I. Puspitasari and Y. Susanti, “Kongruensi Latis Distributif Terkecil pada Semiring dengan Additive Reduct Semilatis,” Pros. Semin. Nas. Aljabar, pp. 55–65, 2016.

Y. Kim and N. Pipattanajinda, “New method for finding the determinant of a matrix,” Chamchuri J. Math., vol. 9, no. January 2017, pp. 1–12, 2017.

S. A. Gyamerah, P. K. Boateng, and P. Harvim, “Max-plus Algebra and Application to Matrix Operations,” Br. J. Math. Comput. Sci., vol. 12, no. 3, pp. 1–14, 2016, doi: 10.9734/bjmcs/2016/21639.

A. W. Nowak, “The Tropical Eigenvalue-Vector Problem from Algebraic, Graphical, and Computational Perspectives,” p. 136, 2014, [Online]. Available: http://scarab.bates.edu/honorstheses/97.

M. A. Rudhito, “Aljabar Max-Plus dan Penerapannya,” 2016.

Subiono, “Aljabar Min-Max Plus dan Terapannya,” p. 173, 2015.

G. Ariyanti, A. Suparwanto, and B. Surodjo, “Karakterisasi Determinan Matriks atas Aljabar Maks Plus Tersimetri,” J. SILOGISME Kaji. Ilmu Mat. dan Pembelajarannya, vol. 3, no. 2, p. 48, 2019, doi: 10.24269/silogisme.v3i2.944.

Siswanto, Pangadi, and S. B. Wiyono, “Robust matrices in the interval max-plus algebra,” J. Phys. Conf. Ser., vol. 1265, no. 1, pp. 1–8, 2019, doi: 10.1088/1742-6596/1265/1/012029.

Siswanto, A. Suparwanto, and M. A. Rudhito, “Strongly regular matrices and simple image set in interval max-plus algebra,” JP J. Algebr. Number Theory Appl., vol. 38, no. 1, pp. 63–78, 2016, doi: 10.17654/NT038010063.

Siswanto, “PERMANEN DAN DOMINAN SUATU MATRIKS ATAS ALJABAR MAX-PLUS INTERVAL,” Pythagoras, vol. 7, no. 2, pp. 45–54, 2012.

Siswanto, “Aturan Cramer dalam Aljabar Maks-Plus Interval,” Mat. J., vol. 20, no. April, pp. 5–11, 2015.

Musthofa and D. Lestari, “Metode Perjanjian Password Berdasarkan Operasi Matriks atas Aljabar Min-Plus untuk Keamanan Pengiriman Informasi Rahasia (The Password Agreement Method Based on Matrix Operation over Min-Plus Algebra for Safety of Secret Information Sending),” J. Sains Dasar, vol. 3, no. 1, pp. 25–33, 2014.

S. Watanabe, “Min-Plus Algebra and Networks,” SpringerReference, vol. 47, pp. 41–54, 2014, doi: 10.1007/springerreference_21127.

S. Siswanto and A. Gusmizain, “Determining the Inverse of a Matrix over Min-Plus Algebra,” JTAM (Jurnal Teor. dan Apl. Mat., vol. 8, no. 1, p. 244, 2024, doi: 10.31764/jtam.v8i1.17432.

A. Gusmizain and S. Wibowo, “Determinant of a matrix over min-plus algebra,” 2021, doi: 10.1080/09720529.2021.1948663.

A. R. Awallia, Siswanto, and V. Y. Kurniawan, “Interval min-plus algebraic structure and matrices over interval min-plus algebra,” J. Phys. Conf. Ser., vol. 1494, no. 1, 2020, doi: 10.1088/1742-6596/1494/1/012010.

M. A. Rudhito and D. A. B. Prasetyo, “Sistem Persamaan Linear Min-Plus Bilangan Kabur dan Penerapannya pada Masalah Lintasan Terpendek dengan Waktu Tempuh Kabur.” Prosiding Seminar Nasional Sains dan Pendidikan Sains IX, pp. 826–834, 2014.

Published
2024-08-02
How to Cite
[1]
A. Septiany, S. Siswanto, and V. Kurniawan, “PERMANENT AND DOMINANT OF MATRIX OVER INTERVAL MIN-PLUS ALGEBRA”, BAREKENG: J. Math. & App., vol. 18, no. 3, pp. 2029-2034, Aug. 2024.
Issue
Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Ade Safira Septiany, Siswanto Siswanto, Vika Yugi Kurniawan

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