Introducing and solving the hesitant fuzzy system AX = B

In this paper the solution for hesitant fuzzy system as AX = B is introduced where A is an n×n known hesitant fuzzy matrix, B is an n×1 known hesitant fuzzy vector and X is an n×1 unknown hesitant fuzzy vector. First, L∞-norm and L1-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.