Summary: In this paper the solution for hesitant fuzzy system as \(AX=B\) is introduced where \(A\) is an \(n\times n\) known hesitant fuzzy matrix, \(B\) is an \(n\times 1\) known hesitant fuzzy vector and \(X\) is an \(n\times 1\) unknown hesitant fuzzy vector.
First, \(L_\infty\)-norm and \(L_1\)-norm of a hesitant fuzzy vector are introduced. Then, the concepts of hesitant fuzzy zero, ‘almost equal’ and ‘less than’ and ‘equal’ are defined for two hesitant fuzzy numbers. Finally, using a minimization problem; the hesitant fuzzy system is solved. At the end, some numerical examples are presented to show the effectiveness of the proposed method.