On the fuzzy solution of LR fuzzy linear systems

In this paper, the solution of fuzzy linear system (FLS) is investigated based on a 11-level expansion. To this end, 11-level of FLS is solved for calculating the core of fuzzy solution and then its spreads are obtained by solving an optimization problem with a special objective function. Using our proposed method, if the computed solution satisfies the FLS, it can be as exact or approximated solution. Finally, the existence of solution of FLS is proved in details and some numerical examples are solved to illustrate the accuracy and capability of the method.