scholarly journals Arbitrary Coupled Trapezoidal Fully Fuzzy Sylvester Matrix Equation

2021 ◽  
Author(s):  
Ahmed Elsayed ◽  
Nazihah Ahmad ◽  
Ghassan Malkawi
Keyword(s):  
Matrix Equation ◽  
Linear Equations ◽  
Matrix Equations ◽  
Sylvester Matrix Equation ◽  
Fuzzy Matrix ◽  
Sylvester Matrix ◽  
Multiplication Operation ◽  
Non Linear ◽  
The Stability ◽  
Non Linear System

Abstract There are many applications where couple of Sylvester matrix equations (CSME) are required to be solved simultaneously, especially in analyzing the stability of control systems. However, there are some situations in which the crisp CSME are not well equipped to deal with the uncertainty problem during the process of stability analysis in control system engineering. Thus, in this paper a new method for solving a coupled trapezoidal fully fuzzy Sylvester matrix equation (CTrFFSME) with arbitrary coefficients is proposed. The arithmetic fuzzy multiplication operation is applied to convert the CTrFFSME into a system of non-linear equations. Then the obtained non-linear system is reduced and converted to a system of absolute equations where the fuzzy solution is obtained by solving that system. The proposed method can solve many unrestricted fuzzy systems such as Sylvester and Lyapunov fully fuzzy matrix equations with triangular and trapezoidal fuzzy numbers. We illustrate the proposed methods by solving numerical example.

scholarly journals Approximate Solution of LR Fuzzy Sylvester Matrix Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Existence Condition ◽  
Sylvester Matrix Equation ◽  
Fuzzy Matrix ◽  
Sylvester Matrix ◽  
Fuzzy Linear System

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.

scholarly journals Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaobin Guo ◽  
Dequan Shang
Keyword(s):  
Matrix Equation ◽  
Symmetric Solution ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Nonsingular Matrix ◽  
Matrix Equations ◽  
System Of Linear Equations ◽  
Fuzzy Matrix ◽  
Fuzzy Linear System ◽  
Product Of Matrices

The fuzzy symmetric solution of fuzzy matrix equationAX˜=B˜, in whichAis a crispm×mnonsingular matrix andB˜is anm×nfuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method.

scholarly journals Two-stage Algorithm for solving Arbitrary Trapezoidal Fully Fuzzy Sylvester Matrix Equations

2021 ◽  
Author(s):  
Ahmed AbdelAziz Elsayed ◽  
Bassem saassouh ◽  
Nazihah Ahmad ◽  
Ghassan Malkawi
Keyword(s):  
Numerical Method ◽  
Matrix Equation ◽  
Fuzzy Numbers ◽  
Linear Equations ◽  
Sylvester Matrix Equation ◽  
Two Stage ◽  
Trapezoidal Fuzzy Numbers ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations ◽  
Fuzzy Solutions

Many authors proposed analytical methods for solving fully fuzzy Sylvester matrix equation (FFSME) based on Vec-operator and Kronecker product. However, these methods are restricted to nonnegative fuzzy numbers and cannot be extended to FFSME with near-zero fuzzy numbers. The main intention of this paper is to develop a new numerical method for solving FFSME with near-zero trapezoidal fuzzy numbers that provides a wider scope of trapezoidal fully fuzzy Sylvester matrix equation (TrFFSME) in scientific applications. This numerical method can solve the trapezoidal fully fuzzy Sylvester matrix equation with arbitrary coefficients and find all possible finite arbitrary solutions for the system. In order to obtain all possible fuzzy solutions, the TrFFSME is transferred to a system of non-linear equations based on newly developed arithmetic fuzzy multiplication between trapezoidal fuzzy numbers. The fuzzy solutions to the TrFFSME are obtained by developing a new two-stage algorithm. To illustrate the proposed method numerical example is solved.

scholarly journals Classification and approximation of solutions to Sylvester matrix equation

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4261-4280 ◽  
Author(s):  
Bogdan Djordjevic ◽  
Nebojsa Dincic
Keyword(s):  
Least Squares ◽  
Matrix Equation ◽  
Infinitely Many Solutions ◽  
Sylvester Matrix Equation ◽  
Minimal Norm ◽  
Sylvester Matrix

In this paperwesolve Sylvester matrix equation with infinitely-many solutions and conduct their classification. If the conditions for their existence are not met, we provide a way for their approximation by least-squares minimal-norm method.

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