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.

在本文中，我们提出了犹豫模糊数（HFN）的新定义，并研究了这些数的一些基本性质。我们显示了（HF）上的（α，k）切分在最近的文献中对HFN的犹豫模糊集（HFS）进行了讨论。在下文中，我们提出了对这些数字的新二进制运算。结果表明，拟议行动的结果是一项最惠国待遇。另外，给出了用于比较两个HFN的新的犹豫模糊关系。最后，在两个示例中介绍了这些数字的一些应用。为此，我们提出了一种解决带有不确定模糊参数的线性规划的新方法。