Intuitionistic hesitant fuzzy set (IHFS) provides a valid mean for dealing with the uncertainty of complex problems. Information measures on IHFS can measure the uncertain information, so that we shall introduce a method to construct a class of distance measures for IHFS in this paper. For constructing more objective distance measures to reflect the actual situation, we consider the information content and information clarity of IHFS simultaneously and utilize different functions to adjust their contribution. Its superiority is evidenced by an example of pattern recognition that the proposed distance measure improves numerically results obtained with existing distance measures. In particular, we investigate the connection between distance measure, similarity measure, and entropy measure of IHFS, and prove that they can be constructed mutually under this axiomatic framework. On this basis, we apply the proposed entropy measure to determine criteria weights in multi-criteria decision-making problems and design an extended intuitionistic hesitant fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) method, which effectiveness is presented by a practical application.

直觉的犹豫模糊集（IHFS）为处理复杂问题的不确定性提供了有效的手段。IHFS的信息量度可以测量不确定信息，因此本文将介绍一种构造IHFS距离量度的方法。为了构建更客观的距离度量以反映实际情况，我们同时考虑了IHFS的信息内容和信息清晰度，并利用不同的功能来调整其贡献。通过模式识别的例子证明了其优越性，即所提出的距离测度可以改善现有距离测度获得的数值结果。特别是，我们研究了IHFS的距离测度，相似度测度和熵测度之间的联系，并证明它们可以在这种公理框架下相互构建。在此基础上，我们将所提出的熵测度用于确定多准则决策问题中的准则权重，并通过类似于理想解决方案（TOPSIS）的方法设计一种用于顺序偏好的扩展直觉犹豫模糊技术。实际应用。