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Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA

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  • Siswanto Siswanto,
  • Ade Safira Septiany
Siswanto Siswanto
Pure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
Ade Safira Septiany
Pure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss1pp571-580
Published January 13, 2025
Keywords
  • Matrix,
  • System of Linear Equations,
  • Cramer's Rule,
  • Interval Min-Plus Algebra
How to Cite
[1]
S. Siswanto and A. S. Septiany, “CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA”, BAREKENG: J. Math. & App., vol. 19, no. 1, pp. 571-580, Jan. 2025.

Copyright (c) 2025 Siswanto Siswanto, Ade Safira Septiany

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

A min-plus algebra is a set ,  where  is the set of all real numbers, equipped with the minimum  and addition  operations. The system of linear equations  in min-plus algebra can be solved using Cramer's rule. Interval min-plus algebra is an extension of min-plus algebra, with the elements in it being closed intervals. The set is denoted by  equipped with two binary operations, namely minimum  and addition . The matrix with notation  is a matrix over interval min-plus algebra with size . Since the structure of min-plus algebra and interval min-plus algebra are analogous, the system of linear equations  in interval min-plus algebra can be solved using Cramer's rule. Based on the research results, the sufficient conditions of Cramer's rule in interval min-plus algebra are  for , and . The Cramer rule is .

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