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Keywords = fuzzy system of linear equations (FSLEs)

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18 pages, 440 KiB  
Article
A Novel Technique to Solve the Fuzzy System of Equations
by Nasser Mikaeilvand, Zahra Noeiaghdam, Samad Noeiaghdam and Juan J. Nieto
Mathematics 2020, 8(5), 850; https://doi.org/10.3390/math8050850 - 24 May 2020
Cited by 15 | Viewed by 3281
Abstract
The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in [...] Read more.
The aim of this research is to apply a novel technique based on the embedding method to solve the n × n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained in two steps. In the first step, if the created n × n crisp linear system has a non-negative solution, the fuzzy linear system will have a fuzzy number vector solution that will be found in the second step by solving another created n × n crisp linear system. Several theorems have been proved to show that the number of operations by the presented method are less than the number of operations by Friedman and Ezzati’s methods. To show the advantages of this scheme, two applicable algorithms and flowcharts are presented and several numerical examples are solved by applying them. Furthermore, some graphs of the obtained results are demonstrated that show the solutions are fuzzy number vectors. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
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9 pages, 1535 KiB  
Article
Numerical Methods for Solving Fuzzy Linear Systems
by Lubna Inearat and Naji Qatanani
Mathematics 2018, 6(2), 19; https://doi.org/10.3390/math6020019 - 1 Feb 2018
Cited by 13 | Viewed by 5012
Abstract
In this article, three numerical iterative schemes, namely: Jacobi, Gauss–Seidel and Successive over-relaxation (SOR) have been proposed to solve a fuzzy system of linear equations (FSLEs). The convergence properties of these iterative schemes have been discussed. To display the validity of these iterative [...] Read more.
In this article, three numerical iterative schemes, namely: Jacobi, Gauss–Seidel and Successive over-relaxation (SOR) have been proposed to solve a fuzzy system of linear equations (FSLEs). The convergence properties of these iterative schemes have been discussed. To display the validity of these iterative schemes, an illustrative example with known exact solution is considered. Numerical results show that the SOR iterative method with ω = 1.3 provides more efficient results in comparison with other iterative techniques. Full article
(This article belongs to the Special Issue Fuzzy Mathematics)
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