Abstract
In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study some essential properties of these numbers. We show (α, k)-cuts that were discussed in the recent literature for hesitant fuzzy sets (HFSs), on HFNs have resulted in compact intervals. In the following, we propose a new binary operation on these numbers. It has shown that the outcome of the proposed operation is a HFN. In addition, a new hesitant fuzzy relationship for comparing two HFNs is given. Finally, some applications of these numbers are presented in two examples. For this purpose, we propose a new approach to solve linear programming with hesitant fuzzy parameters.
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