Fuzzy linear matrix equation

Allahviranloo, Tofigh; Mikaeilvand, Nasser; Barkhordary, M.

doi:10.1007/s10700-009-9058-1

Cited by 26 publications

(12 citation statements)

References 20 publications

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“…In order to solve the fuzzy matrix equation ( 3), we need to consider the systems of linear equations (21) or (26). It seems that we have obtained the minimal solution of the function linear system (21) as…”

Section: By the Matrix Operation The Above Linear Matrix Equations Are Equivalent Withmentioning

confidence: 99%

“…So, the investigation on fuzzy matrix systems has been paid attention by some scholars in past decades. In 2009, Allahviranloo et al [21] investigated the fuzzy matrix equation, A 􏽥 XB � 􏽥 C. In 2018, AmirfakhrianIn et al [22] presented a new algorithm for calculating the fuzzy linear matrix equation with the form A 􏽥 XB � 􏽥 C by another way. In 2011, Gong and Guo [23] discussed inconsistent fuzzy linear systems and studied its least squares fuzzy solution.…”

Section: Introductionmentioning

confidence: 99%

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Solving Complex Fuzzy Linear Matrix Equations

Sun

Xiao

2021

Mathematical Problems in Engineering

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In this paper, a kind of complex fuzzy linear matrix equation A X ˜ B = C ˜ , in which C ˜ is a complex fuzzy matrix and A and B are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.

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Section: By the Matrix Operation The Above Linear Matrix Equations Are Equivalent Withmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Solving Complex Fuzzy Linear Matrix Equations

Sun

Xiao

2021

Mathematical Problems in Engineering

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“…Abbasbany et al in [11][12][13], applied the decomposition method and steepest descent method for solving this problem. 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.…”

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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“…In recent years, T. Allahviranloo, N. Babbar et al [13][14] proposed many new approaches and theories of fuzzy linear systems. In 2009, Allahviranloo et al [15] firstly discussed the fuzzy linear matrix equations (FLME) with form of C B X A by the Kronecker product of the matrices. In 2011, Gong and Guo [16]…”

Section: Introductionmentioning

confidence: 99%

Approximate Solution of LR Fuzzy Matrix System

Shang¹,

Wei²,

Xiao

2018

Proceedings of the 2018 3rd International Conference on Modelling, Simulation and Applied Mathematics (MSAM 2018)

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In this paper we proposed a general model for solving the fuzzy matrix equation AX=B in which A is a crisp matrix and B is an arbitrary LR fuzzy numbers matrix. The original fuzzy equation is converted to a system of linear matrix equations by the embedding approach. The fuzzy solution is derived from solving model and a sufficient condition for the existence of strong LR fuzzy solution is analyzed. Two illustrating examples are given to show the effectiveness of the proposed method.

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Fuzzy linear matrix equation

Cited by 26 publications

References 20 publications

Solving Complex Fuzzy Linear Matrix Equations

Solving Complex Fuzzy Linear Matrix Equations

A Novel Technique to Solve the Fuzzy System of Equations

Approximate Solution of LR Fuzzy Matrix System

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