As an extension of the fuzzy set, the hesitant fuzzy set (HFS) is an effective tool for handling uncertainty and vagueness in decision making problems. Considering that the correlation coefficient (CC) has a strong ability to process and analyze data, we are developing a novel CC to measure the strength of the relationship between HFSs in this article. The CC presented between the HFSs has more desirable properties than the current ones. It relaxes limits on the length of the hesitant fuzzy elements (HFEs) and can be used to determine whether the HFSs are negatively or positively correlated. More importantly, it can ensure that the CC between two HFSs is equal to one (minus one) if and only if the two HFSs are the same (complement each other), and thus avoid the achievement of counter-intuitive decision results by inappropriate calculation approaches. The motivation of re-visiting the CC between HFSs is that a more effective CC between HFSs should be developed in order to significantly improve decision-making performance. To demonstrate the effectiveness of the proposed method, a case study on medical diagnosis is offered and the comparative analyses with other methods are also conducted.

作为模糊集的扩展，犹豫模糊集（HFS）是处理决策问题中的不确定性和模糊性的有效工具。考虑到相关系数（CC）具有很强的数据处理和分析能力，我们正在开发一种新颖的CC来衡量本文中HFS之间关系的强度。HFS 之间呈现的 CC 具有比当前更理想的属性。它放宽了对犹豫模糊元素 (HFE) 长度的限制，可用于确定 HFS 是负相关还是正相关。更重要的是，它可以保证两个HFS之间的CC等于1（减1），当且仅当两个HFS相同（互补），从而避免通过不适当的计算方法获得违反直觉的决策结果。重新访问 HFS 之间的 CC 的动机是应该开发 HFS 之间更有效的 CC，以便显着提高决策性能。为了证明所提出方法的有效性，提供了一个医学诊断案例研究，并与其他方法进行了比较分析。