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CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 1 (2025) · pp. 571–580

DOI
10.30598/barekengvol19iss1pp571-580
ISSN
2615-3017, 1978-7227
Published
2025-01-13
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

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.

Collaboration network of the authors

40 authors · 126 co-authorship links · 5 across different organisations · showing the 40 most connected

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Padjadjaran University
  • Sekolah Tinggi Agama Islam Syubbanul Wathon Magelang
  • Universitas Halu Oleo
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Anisa KalondengAffiliation unknown4
Sri Astuti ThamrinAffiliation unknown3
Vika Yugi KurniawanAffiliation unknown3
Sitti SahrimanAffiliation unknown2
Andi Isna YunitaAffiliation unknown2
Andi M Alfin BasoAffiliation unknown2
M. Zaky Hisyam GozhiAffiliation unknown2
Nurtiti SunusiAffiliation unknown2
Raupong RaupongAffiliation unknown2
Surya GumilarAffiliation unknown2
Muhamad SholikhunSekolah Tinggi Agama Islam Syubbanul Wathon Magelang1
Zulfatus SorayaAffiliation unknown1
Milna WafirahSekolah Tinggi Agama Islam Syubbanul Wathon Magelang1
Budi AyuningsihPadjadjaran University1
Iman HernamanPadjadjaran University1
Tidi DhalikaPadjadjaran University1
Destu Putra RosmawanAffiliation unknown1
Dedi RahmatPadjadjaran University1
Ansharullah AnsharullahUniversitas Halu Oleo1
Abdu Rahman BacoAffiliation unknown1
Alfiana AntohAffiliation unknown1
Yundy HafizriandaAffiliation unknown1
Anna IslamiyatiAffiliation unknown1
Hajratul Ashwad KAffiliation unknown1
Afifah Mutiah NurdinAffiliation unknown1
Muh. Indirwan ArfanAffiliation unknown1
Muhammad FadilAffiliation unknown1
A.Muthiah Nur AngrianyAffiliation unknown1
Rini JamalAffiliation unknown1
Andi FebriyantiAffiliation unknown1
Rahmiati RahimAffiliation unknown1
Nirwan IlyasAffiliation unknown1
Haksar HaksarAffiliation unknown1
Nurhaliza RaisAffiliation unknown1
Maryana MaharaniAffiliation unknown1
Rahmat HermawanAffiliation unknown1
Fadlan AminAffiliation unknown1
Ahmad Ryan Al AqshaAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc)
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	<dc:title xml:lang="en-US">CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA</dc:title>
	<dc:creator>Siswanto, Siswanto</dc:creator>
	<dc:creator>Septiany, Ade Safira</dc:creator>
	<dc:description xml:lang="en-US">A min-plus algebra is a set  , &amp;nbsp;where  &amp;nbsp;is the set of all real numbers, equipped with the minimum  &amp;nbsp;and addition  &amp;nbsp;operations. The system of linear equations  &amp;nbsp;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  &amp;nbsp;equipped with two binary operations, namely minimum  &amp;nbsp;and addition  . The matrix with notation  &amp;nbsp;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  &amp;nbsp;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  &amp;nbsp;for  , and  . The Cramer rule is  .</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-01-13</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14863</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss1pp571-580</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application; 571-580</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss1year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14863/9552</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Siswanto Siswanto, Ade Safira Septiany</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>