An efficient method for solving LR fuzzy dual matrix systems

Abstract

In this paper, the fuzzy dual matrix system as $A\tilde{x}+\tilde{B}=C\tilde{x}+\tilde{D}$ in which A, C are n × n crisp matrices and $\tilde{B}$, $\tilde{D}$ are n × n LR fuzzy matrices is studied. To obtain the solution of fuzzy dual system, we initially solve 1-cut and use minimization problem to calculate the spreads. Afterwards, we explain the relationship between the solutions of the systems of $A\tilde{x}+\tilde{B}=C\tilde{x}+\tilde{D}$ and $(A-C)\tilde{x}=\left(\tilde{D}\underset{h}{\ominus }\tilde{B}\right)$. Finally, some examples are solved to illustrate the proposed method.