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SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 2 (2025) · pp. 1169–1178

DOI
10.30598/barekengvol19iss2pp1169-1178
ISSN
2615-3017, 1978-7227
Published
2025-04-01
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

A system of nonlinear equations is a collection of several interrelated non-linear equations. Currently, systems of nonlinear equations are used not only on crisp but also on fuzzy numbers. A fuzzy number is an ordered pair function that has a degree of membership [0,1]. Meanwhile, a fully fuzzy system of equations is a system of equations that applies fuzzy number arithmetic operations. The solution of non-linear equation systems is usually complicated to solve analytically, so numerical methods are used as an alternative to solve these problems. In this research, the steps to find the solution of nonlinear fully fuzzy equation systems using genetic algorithms are studied, which in the solution process is based on the theory of evolution and natural selection. The solution steps taken are first converting the fully fuzzy system of equations into a system of crisp equations, next constructing the system of strict equations as a multi-objective optimization problem, and lastly solving the optimization problem using a genetic algorithm which includes initialization, evaluation, selection, crossover, and mutation. As illustrations, several cases of nonlinear fully fuzzy and dual fully fuzzy systems of equations on triangular fuzzy numbers and trapezoidal fuzzy numbers are given. The approximate solutions obtained using genetic algorithms produce solutions that are close to their analytic solutions.

Collaboration network of the authors

15 authors · 29 co-authorship links

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  • Lampung University
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Dorrah AzisAffiliation unknown1
Tiryono RubyAffiliation unknown1
Muhammad Is’ad ArifaldiAffiliation unknown1
Elvina HalimAffiliation unknown1
Dian KurniasariLampung University1
Mustofa UsmanLampung University1
Virda KurniawatiAffiliation unknown1
Rizki Khoirun NisaAffiliation unknown1
Fachri FaisalAffiliation unknown1
Baki SwitaAffiliation unknown1
Mulia AstutiAffiliation 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">SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM</dc:title>
	<dc:creator>Fatimatuzzahra, Fatimatuzzahra</dc:creator>
	<dc:creator>Nuryaman, Aang</dc:creator>
	<dc:creator>Zakaria, La</dc:creator>
	<dc:creator>Sutrisno, Agus</dc:creator>
	<dc:description xml:lang="en-US">A system of nonlinear equations is a collection of several interrelated non-linear equations. Currently, systems of nonlinear equations are used not only on crisp but also on fuzzy numbers. A fuzzy number is an ordered pair function that has a degree of membership [0,1]. Meanwhile, a fully fuzzy system of equations is a system of equations that applies fuzzy number arithmetic operations. The solution of non-linear equation systems is usually complicated to solve analytically, so numerical methods are used as an alternative to solve these problems. In this research, the steps to find the solution of nonlinear fully fuzzy equation systems using genetic algorithms are studied, which in the solution process is based on the theory of evolution and natural selection. The solution steps taken are first converting the fully fuzzy system of equations into a system of crisp equations, next constructing the system of strict equations as a multi-objective optimization problem, and lastly solving the optimization problem using a genetic algorithm which includes initialization, evaluation, selection, crossover, and mutation. As illustrations, several cases of nonlinear fully fuzzy and dual fully fuzzy systems of equations on triangular fuzzy numbers and trapezoidal fuzzy numbers are given. The approximate solutions obtained using genetic algorithms produce solutions that are close to their analytic solutions.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-04-01</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/15419</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss2pp1169-1178</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application; 1169-1178</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss2year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15419/9948</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Fatimatuzzahra Fatimatuzzahra, Aang Nuryaman, La Zakaria, Agus Sutrisno</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
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