Approximate Solution of LR Fuzzy Sylvester Matrix Equations

Xiao, Guo; Shang, Dequan

doi:10.1155/2013/752760

Cited by 9 publications

(7 citation statements)

References 30 publications

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“…This matrix equation contributed significantly in control theory (Benner 2004;Darouach 2006). A study was conducted by Shang et al (2015), who applied a concept of arithmetic multiplication operator previously demonstrated by Dehghan et al (2006)and Guo and Shang (2013) in solving FFLS and FME respectively. This operator converts the FFSE into a crisp form of Sylvester matrix equation where the solutions are then obtained using the Kronecker product of matrices where the multiplication operator provided the simpler method which is easy to handle by most of the researchers.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, alternative methods for solving FFSME have been proposed by (Malkawi et al 2015c). Contrary to (Guo and Shang 2013), their research shows that FFSME is converted to FFLS using the Kronecker product and applying their proposed linear system method. In (Malkawi et al 2014), the FFLS was transformed to a linear systems where the solution is obtained by the matrix inversion method.…”

Section: Introductionmentioning

confidence: 99%

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On the solution of fully fuzzy Sylvester matrix equation with trapezoidal fuzzy numbers

2020

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Sylvester matrix equations play a prominent role in various areas such as control theory, medical imaging acquisition systems, model reduction, and stochastic control. Considering any uncertainty problems such as conflicting requirements during system process, instability of environmental conditions, distraction of any elements and noise, all for which the classical matrix equation is sometimes ill-equipped, fuzzy numbers represent the most effective tool that can be used to model matrix equations in the form of fuzzy equations. In most of the previous literature, the solutions of fuzzy systems are only presented with triangular fuzzy numbers. In this paper, we discuss fully fuzzy Sylvester matrix equation with positive and negative trapezoidal fuzzy numbers. An analytical approach for solving a fully fuzzy Sylvester matrix equation is proposed by transforming the fully fuzzy matrix equation into a system of four crisp Sylvester linear matrix equation. In obtaining the solution the Kronecker product and Vec-operator are used. Numerical examples are solved to illustrate the proposed method.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the solution of fully fuzzy Sylvester matrix equation with trapezoidal fuzzy numbers

2020

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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 the past decade, some researchers paid more attention to LR fuzzy linear systems. In 2013, Guo and Shang [22] proposed a computing method for the fuzzy Sylvester matrix equations +̃=̃with LR fuzzy numbers. Later, Gong et al [23] studied the general dual fuzzy linear matrix systems̃+̃= +̃based on LR fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Minimal Solution of Complex Fuzzy Linear Systems

Xiao

Zhang

2016

Advances in Fuzzy Systems

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This paper investigates the complex fuzzy linear equation Cz~=w~ in which C is a crisp complex matrix and w~ is an arbitrary LR complex fuzzy vector. The complex fuzzy linear system is converted to equivalent high order fuzzy linear system Gx~=b~. A new numerical procedure for calculating the complex fuzzy solution is designed and a sufficient condition for the existence of strong complex fuzzy solution is derived in detail. Some examples are given to illustrate the proposed method.

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Approximate Solution of LR Fuzzy Sylvester Matrix Equations

Cited by 9 publications

References 30 publications

On the solution of fully fuzzy Sylvester matrix equation with trapezoidal fuzzy numbers

On the solution of fully fuzzy Sylvester matrix equation with trapezoidal fuzzy numbers

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

Minimal Solution of Complex Fuzzy Linear Systems

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