Solving Complex Fuzzy Linear Matrix Equations

Abstract

In this paper, a kind of complex fuzzy linear matrix equation $A\tilde{X}B=\tilde{C}$ , in which $\tilde{C}$ is a complex fuzzy matrix and $A$ and $B$ are crisp matrices, is investigated by using a matrix method. The complex fuzzy matrix equation is extended into a crisp system of matrix equations by means of arithmetic operations of fuzzy numbers. Two brand new and simplified procedures for solving the original fuzzy equation are proposed and the correspondingly sufficient condition for strong fuzzy solution are analysed. Some examples are calculated in detail to illustrate our proposed method.