Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

Xiao, Guo; Shang, Dequan

doi:10.1155/2012/318069

Cited by 13 publications

(10 citation statements)

References 26 publications

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“…Example 15. Consider the fully fuzzy linear matrix system 17,12,23) LR (22,22,29) LR (17,16,28) LR (19,15,13) LR (23,23,16) LR (19,16,17) LR ) .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…By using the parametric form of fuzzy number, they derived necessary and sufficient conditions for the existence condition of fuzzy solutions and designed a numerical procedure for calculating the solutions of the fuzzy matrix equations. In 2011, Guo et al [27][28][29] investigated a class of fuzzy matrix equations =̃by means of the block Gaussian elimination method and studied the least squares solutions of the inconsistent fuzzy matrix equatioñ=̃by using generalized inverses of the matrix, and discussed fuzzy symmetric solutions of fuzzy matrix equations̃=̃. What is more, there are two shortcomings in the above fuzzy systems.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

Xiao

Shang

2013

Journal of Applied Mathematics

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The fuzzy matrix equationsA~⊗X~⊗B~=C~in whichA~,B~, andC~arem×m,n×n, andm×nnonnegative LR fuzzy numbers matrices, respectively, are investigated. The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. In addition, the existence condition of nonnegative fuzzy solution is discussed. Two examples are calculated to illustrate the proposed method.

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“…Example 15. Consider the fully fuzzy linear matrix system 17,12,23) LR (22,22,29) LR (17,16,28) LR (19,15,13) LR (23,23,16) LR (19,16,17) LR ) .…”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

Xiao

Shang

2013

Journal of Applied Mathematics

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“…To date, considerable work has been conducted on matrix equations, such as the fuzzy matrix equation (FME), AX m =B m [17], and fuzzy Sylvester matrix equation (FSE), AX +XB =C [2,15,16,18,19,27].…”

Section: Introductionmentioning

confidence: 99%

A new solution of pair matrix equations with arbitrary triangular fuzzy numbers

Daud¹,

Ahmad²,

Malkawi³

2019

Turk J Math

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Pair matrix equations have numerous applications in control system engineering, such as for stability analysis of linear control systems and also for reduction of nonlinear control system models. There are some situations in which the classical pair matrix equations are not well equipped to deal with the uncertainty problem during the process of stability analysis and reduction in control system engineering. Thus, this study presents a new algorithm for solving fully fuzzy pair matrix equations where the parameters of the equations are arbitrary triangular fuzzy numbers. The fuzzy Kronecker product and fuzzy V ec-operator are employed to transform the fully fuzzy pair matrix equations to a fully fuzzy pair linear system. Then a new associated linear system is developed to convert the fully fuzzy pair linear system to a crisp linear system. Finally, the solution is obtained by using a pseudoinverse method. Some related theoretical developments and examples are constructed to illustrate the proposed algorithm. The developed algorithm is also able to solve the fuzzy pair matrix equation.

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“…In 2011, Guo [24] studied the approximate solution of fuzzy Sylvester matrix equations with triangular fuzzy numbers. Lately, Guo and Shang [25] considered the fuzzy symmetric solutions of fuzzy matrix equatioñ=̃.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solution of LR Fuzzy Sylvester Matrix Equations

Xiao

Shang

2013

Journal of Applied Mathematics

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The fuzzy Sylvester matrix equationAX~+X~B=C~in whichA,Barem×mandn×ncrisp matrices, respectively, andC~is anm×nLR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.

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Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

Cited by 13 publications

References 26 publications

Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

A new solution of pair matrix equations with arbitrary triangular fuzzy numbers

Approximate Solution of LR Fuzzy Sylvester Matrix Equations

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