Approximate Solution of LR Fuzzy Sylvester Matrix Equations

Abstract

The fuzzy Sylvester matrix equation $A\tilde{X}+\tilde{X}B=\tilde{C}$ in which $A,B$ are $m\times m$ and $n\times n$ crisp matrices, respectively, and $\tilde{C}$ is an $m\times n$ LR 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.