Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations

Abstract

The fuzzy matrix equations $\tilde{A}\otimes \tilde{X}\otimes \tilde{B}=\tilde{C}$ in which $\tilde{A}$, $\tilde{B}$, and $\tilde{C}$ are $m\times m$, $n\times n$, and $m\times n$ nonnegative 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.