CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA
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...
| 出版年: | Barekeng |
|---|---|
| 主要な著者: | , |
| フォーマット: | 論文 |
| 言語: | 英語 |
| 出版事項: |
Universitas Pattimura
2025-01-01
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| 主題: | |
| オンライン･アクセス: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14863 |
| _version_ | 1849432086518169600 |
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| author | Siswanto Siswanto Ade Safira Septiany |
| author_facet | Siswanto Siswanto Ade Safira Septiany |
| author_sort | Siswanto Siswanto |
| collection | DOAJ |
| container_title | Barekeng |
| description | 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 . |
| format | Article |
| id | doaj-art-a441fc6641b246e9b449ea490d7eefb8 |
| institution | Directory of Open Access Journals |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| spelling | doaj-art-a441fc6641b246e9b449ea490d7eefb82025-08-20T03:37:34ZengUniversitas PattimuraBarekeng1978-72272615-30172025-01-0119157158010.30598/barekengvol19iss1pp571-58014863CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRASiswanto Siswanto0Ade Safira Septiany1Pure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, IndonesiaPure Mathematics and Application Research Group, Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, IndonesiaA 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 .https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14863matrixsystem of linear equationscramer's ruleinterval min-plus algebra |
| spellingShingle | Siswanto Siswanto Ade Safira Septiany CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA matrix system of linear equations cramer's rule interval min-plus algebra |
| title | CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA |
| title_full | CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA |
| title_fullStr | CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA |
| title_full_unstemmed | CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA |
| title_short | CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA |
| title_sort | cramer s rule in interval min plus algebra |
| topic | matrix system of linear equations cramer's rule interval min-plus algebra |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14863 |
| work_keys_str_mv | AT siswantosiswanto cramersruleinintervalminplusalgebra AT adesafiraseptiany cramersruleinintervalminplusalgebra |