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Article

A Novel Technique to Solve the Fuzzy System of Equations

1
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran
2
Department of Mathematics and Computer Science, Shahed University, Tehran, Iran
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Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, Chelyabinsk 454080, Russia
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Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk, Russia
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Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 850; https://doi.org/10.3390/math8050850
Received: 15 April 2020 / Revised: 20 May 2020 / Accepted: 21 May 2020 / Published: 24 May 2020
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
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. View Full-Text
Keywords: fuzzy linear system; fuzzy number; fuzzy number vector; embedding method fuzzy linear system; fuzzy number; fuzzy number vector; embedding method
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MDPI and ACS Style

Mikaeilvand, N.; Noeiaghdam, Z.; Noeiaghdam, S.; Nieto, J.J. A Novel Technique to Solve the Fuzzy System of Equations. Mathematics 2020, 8, 850. https://doi.org/10.3390/math8050850

AMA Style

Mikaeilvand N, Noeiaghdam Z, Noeiaghdam S, Nieto JJ. A Novel Technique to Solve the Fuzzy System of Equations. Mathematics. 2020; 8(5):850. https://doi.org/10.3390/math8050850

Chicago/Turabian Style

Mikaeilvand, Nasser, Zahra Noeiaghdam, Samad Noeiaghdam, and Juan J. Nieto 2020. "A Novel Technique to Solve the Fuzzy System of Equations" Mathematics 8, no. 5: 850. https://doi.org/10.3390/math8050850

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