The nearest symmetric fuzzy solution for a symmetric fuzzy linear system

In this paper, the nearest symmetric fuzzy solution for a symmetric L-L fuzzy linear system (S-L-FLS) is obtained by a new metric. To this end, the S-L-FLS is transformed to the non-linear programming problem (NLP). The solution of the obtained NLP is our favorite fuzzy number vector solution. Also, it is shown that if an S-L-FLS has unique fuzzy solution, then its solution is symmetric. Two constructive algorithms are presented in details and the method is illustrated by solving several numerical examples