Solving fuzzy matrix equation of the form X ˜ A = B ˜

Solving Complex Fuzzy Linear Matrix Equations

“…In order to solve the fuzzy matrix equation ( 3), we need to consider the systems of linear equations (21) or (26). It seems that we have obtained the minimal solution of the function linear system (21) as…”

“…from equations (28) or (29), may still not be an appropriate complex fuzzy matrix except that both 􏽥 M and 􏽥 N are appropriate fuzzy number matrices. Restricting the discussion to the complex triangular fuzzy numbers, i.e., m ij (r), m ij (r), 1 ≤ i, j ≤ n, and consequently n ij (r), n ij (r), 1 ≤ i, j ≤ n are all linear functions of r, and having calculated X(r) which solves (21) or (26), we define the complex fuzzy minimal solution to the fuzzy linear matrix equation (3) as follows. Definition 8.…”

“…Definition 8. Let X(r) � (m ij (r), m ij (r)) + i(n ij (r), n ij (r)), 1 ≤ i, j ≤ n be the minimal solution of model ( 21) or (26). e complex fuzzy number matrix 􏽥 W � (p ij (r), p ij (r)) + i(q ij (r), q ij (r)), 1 ≤ i, j ≤ n 􏼚 defined by…”

“…In 2014, Gong et al [24] studied the general dual fuzzy matrix systems A 􏽥 X + 􏽥 B � C 􏽥 X + 􏽥 D based on the LR fuzzy numbers. In 2017, Guo et al [25,26] studied the fuzzy matrix system of the form 􏽥 XA � 􏽥 B by a matrix method and made a further investigation to dual fuzzy matrix equation…”

Inconsistent LR Fuzzy Matrix Equation

“…In 2014, Gong and Guo et al [31] studied the general dual fuzzy matrix systems AX + B � CX + D according to arithmetic operations of LR fuzzy numbers. In 2017, Guo et al [32,33] studied the fuzzy matrix equation with the form of XA � B by a matrix method and made a further investigation to dual fuzzy matrix equation AX + B � CX + D. In 2018, Guo and Shang [34] introduced a class of complex fuzzy matrix equation ZC � W and proposed a general model to deal with it. Recently, Guo et al [35] proposed a new method for solving linear fuzzy matrix equations AXB � C based on LR fuzzy numbers.…”