scholarly journals Trapezoidal Fully Fuzzy Sylvester Matrix Equation with Arbitrary Coefficients

2021 ◽  
Author(s):  
Ahmed Elsayed ◽  
Nazihah Ahmad ◽  
Ghassan Malkawi
Keyword(s):  
Linear Equation ◽  
Matrix Equation ◽  
Analytical Methods ◽  
Fuzzy Numbers ◽  
Coefficient Matrix ◽  
Sylvester Matrix Equation ◽  
Numerical Examples ◽  
Trapezoidal Fuzzy Numbers ◽  
Sylvester Matrix ◽  
Methods Numerical

Abstract Almost every existing method for solving trapezoidal fully fuzzy Sylvester matrix equation restricts the coefficient matrix and the solution to be positive fuzzy numbers only. In this paper, we develop new analytical methods to solve a trapezoidal fully fuzzy Sylvester matrix equation with restricted and unrestricted coefficients. The trapezoidal fully fuzzy Sylvester matrix equation is transferred to a system of crisp equations based on the sign of the coefficients by using Ahmd arithmetic multiplication operations between trapezoidal fuzzy numbers. The constructed method not only obtain a simple crisp system of linear equation that can be solved by any classical methods but also provide a widen the scope of the trapezoidal fully fuzzy Sylvester matrix equation in scientific applications. Furthermore, these methods have less steps and conceptually easy to understand when compared with existing methods. To illustrate the proposed methods numerical examples are solved.

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 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.

SOME NEW COMPUTATIONAL METHODS TO SOLVE DUAL FULLY FUZZY LINEAR SYSTEM OF ARBITRARY TRIANGULAR FUZZY NUMBERS

2013 ◽  
Vol 09 (01) ◽  
pp. 13-26 ◽  
Author(s):  
AMIT KUMAR ◽  
BABBAR NEETU ◽  
ABHINAV BANSAL
Keyword(s):  
Linear System ◽  
Computational Methods ◽  
Fuzzy Numbers ◽  
Coefficient Matrix ◽  
Computational Techniques ◽  
Triangular Fuzzy Numbers ◽  
Numerical Examples ◽  
Fully Fuzzy Linear System ◽  
Fuzzy Linear System ◽  
Methods Numerical

In this paper, we discuss two new computational techniques for solving a generalized fully fuzzy linear system (FFLS) with arbitrary triangular fuzzy numbers (m,α,β). The methods eliminate the non-negative restriction on the fuzzy coefficient matrix that has been considered by almost every method in the literature and relies on the decomposition of the dual FFLS into a crisp linear system that can be further solved by a variety of classical methods. To illustrate the proposed methods, numerical examples are solved and the obtained results are discussed. The methods pose several advantages over the existing methods to solve a simple or dual FFLS.

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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