Analyzing the solution of a system of fuzzy linear equations by a fuzzy distance

Amirfakhrian, Majid

doi:10.1007/s00500-012-0801-0

Cited by 15 publications

(2 citation statements)

References 38 publications

(26 reference statements)

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“…Allahviranloo et al in [14][15][16][17][18], studied the fuzzy numbers and its application for solving fuzzy linear systems and a fuzzy matrix equation in the form AXB = C. In [19], some conditions of the existence of a fuzzy or interval solution of the m × n linear system were derived and in [20], the inner estimation of the solution set of a fuzzy linear system was found. Amirfakhrian in [21] considered the FSLEs by fuzzy distance, in [22] he presented the numerical solution of the FSLEs in the polynomial parametric form, and in [23] he studied the fuzzy matrix equations. Fariborzi Araghi et al in [24] applied the inherited LU factorization, Mikaeilvand and Noeiaghdam in [25][26][27] discussed the fuzzy linear matrix equations, general solutions of m × n fuzzy linear systems, and least square solutions of inconsistent fuzzy linear matrix equations.…”

Section: Introductionmentioning

confidence: 99%

A Novel Technique to Solve the Fuzzy System of Equations

Mikaeilvand

Noeiaghdam

et al. 2020

Mathematics

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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.

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Section: Introductionmentioning

confidence: 99%

A Novel Technique to Solve the Fuzzy System of Equations

Mikaeilvand

Noeiaghdam

et al. 2020

Mathematics

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“…In 1998, Friedman et al [18] presented a model to solve the FSLEs and many mathematicians improved and developed this method to find the solution of FSLEs. In last years, Friedman et al [18,19,21], Abbasbany et al [1,2,9], Allahviranloo et al [3,4,5,6,7] and others [8,12,13,22,23,26,31,32] considered the n × n FSLEs. Also, many authors applied the numerical methods to find the approximate solution of the FSLEs [1,2,20,27,29].…”

Section: Introductionmentioning

confidence: 99%

A novel technique to solve the fuzzy system of equations

Mikaeilvand,

Noeiaghdam,

Noeiaghdam

et al. 2018

Preprint

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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 by transforming the n × n FSLE to the crisp system. In this paper, Ezzati's method to solve the FSLEs is modified and improved. Several theorems are proved to show the number of operations for presented method are less than the methods of Friedman and Ezzati. In order to show the advantages of scheme, two applicable algorithms are presented and several examples are solved by applying them. Also, some graphs of obtained results are demonstrated which show the solutions are in the fuzzy form.

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