SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM
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 sys...
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Universitas Pattimura
2025-04-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15419 |
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| author | Fatimatuzzahra Fatimatuzzahra Aang Nuryaman La Zakaria Agus Sutrisno |
| author_facet | Fatimatuzzahra Fatimatuzzahra Aang Nuryaman La Zakaria Agus Sutrisno |
| author_sort | Fatimatuzzahra Fatimatuzzahra |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8c7ac5dad3ca4e15bea8cc416e5f0827 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-8c7ac5dad3ca4e15bea8cc416e5f08272025-08-20T04:01:48ZengUniversitas PattimuraBarekeng1978-72272615-30172025-04-011921169117810.30598/barekengvol19iss2pp1169-117815419SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHMFatimatuzzahra Fatimatuzzahra0Aang Nuryaman1La Zakaria2Agus Sutrisno3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Lampung, IndonesiaA 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.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15419fully fuzzy nonlinear equation systemsfuzzy numbersgenetic algorithmoptimization problems |
| spellingShingle | Fatimatuzzahra Fatimatuzzahra Aang Nuryaman La Zakaria Agus Sutrisno SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM Barekeng fully fuzzy nonlinear equation systems fuzzy numbers genetic algorithm optimization problems |
| title | SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM |
| title_full | SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM |
| title_fullStr | SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM |
| title_full_unstemmed | SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM |
| title_short | SOLUTION OF FULLY FUZZY NONLINEAR EQUATION SYSTEMS USING GENETIC ALGORITHM |
| title_sort | solution of fully fuzzy nonlinear equation systems using genetic algorithm |
| topic | fully fuzzy nonlinear equation systems fuzzy numbers genetic algorithm optimization problems |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/15419 |
| work_keys_str_mv | AT fatimatuzzahrafatimatuzzahra solutionoffullyfuzzynonlinearequationsystemsusinggeneticalgorithm AT aangnuryaman solutionoffullyfuzzynonlinearequationsystemsusinggeneticalgorithm AT lazakaria solutionoffullyfuzzynonlinearequationsystemsusinggeneticalgorithm AT agussutrisno solutionoffullyfuzzynonlinearequationsystemsusinggeneticalgorithm |