A Novel Technique to Solve the Fuzzy System of Equations

Nasser Mikaeilvand, Zahra Noeiaghdam, Samad Noeiaghdam and Juan J. Nieto
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Nasser Mikaeilvand: Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran
Zahra Noeiaghdam: Department of Mathematics and Computer Science, Shahed University, Tehran, Iran
Samad Noeiaghdam: Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, Chelyabinsk 454080, Russia
Juan J. Nieto: Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Mathematics, 2020, vol. 8, issue 5, 1-18

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 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.

Keywords: fuzzy linear system; fuzzy number; fuzzy number vector; embedding method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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