To characterize the uncertainty of a hesitant fuzzy set, a new entropy, which is called (R, S)-norm information measure, is proposed in this paper. It is proved that the proposed measure satisfies the axiomatic definition of entropy measures for hesitant fuzzy sets, and then, some properties of the proposed measure are also explored. Furthermore, several examples are presented to show the advantages of the (R, S)-norm information measure compared with some existing entropy measures. Then, based on the new information measure, we utilize decision-making method by combining prospect theory with technique for order preference by similarity to an ideal solution to address multi-attribute decision-making problems. Finally, a concrete example of business investment is provided to illustrate the effectiveness of our proposed information measure, and comparative analysis is also completed to verify the validity of the (R, S)-norm information measure.

为了描述犹豫模糊集的不确定性，提出了一种新的熵，称为（R，  S）范数信息测度。证明了所提出的测度满足犹豫模糊集的熵测度的公理定义，然后，对该拟测度的一些性质进行了探索。此外，还提供了几个示例来展示（R，  S）规范信息测度与一些现有的熵测度相比。然后，基于新的信息测度，我们通过将前景理论与技术相结合的决策方法，通过相似的理想偏好来解决订单偏好问题，从而解决多属性决策问题。最后，提供了一个商业投资的具体例子来说明我们提出的信息测度的有效性，并完成了比较分析以验证（R，  S）规范信息测度的有效性。