Abstract: Intuitionistic hesitant fuzzy sets (IHFSs), synthesizing the advantages of intuitionistic fuzzy sets and hesitant fuzzy sets, express the inconsistent preferences for decision makers more effectively. However, there is little research on the distance measures between IHFSs despite the fact that distance measure has received close attention, so the Hamming distance, Euclidean distance and generalized distance between two IHFSs are defined. Besides, we define the generalized weighted distance if the weight of each element is taken into account. Considering that hesitancy is the fundamentally characteristic of IHFSs, several novel distance measures which take the hesitancy degree into account are defined, in which both the values of intuitionistic hesitant fuzzy numbers (IHFNs) and the hesitancy degree are taken into account. The distance measure with preference can be calculated by setting different preference values between the values of IHFNs and the hesitancy degree if decision makers have different preference. Then we introduce an extended TOPSIS method based on new distance measures under intuitionistic hesitant fuzzy environment. Finally, a numerical example is given to show the reasonability and applicability of the proposed method.

Key words: intuitionistic hesitant fuzzy sets, distance measure, hesitancy degree, TOPSIS method

摘要： 直觉犹豫模糊集集成了直觉模糊集和犹豫模糊集的优势,能更有效地刻画决策者偏好不一致的情况。距离测度一直是研究的热点问题,但尚没有文献研究直觉犹豫模糊集间的距离测度,因此本文定义了直觉犹豫模糊集间的Hamming距离、Euclidean距离和广义距离,同时考虑每个元素的权重,定义了加权距离。犹豫度是直觉犹豫模糊集的重要特性,因此在考虑犹豫度的基础上,又定义了一些距离测度。这些距离测度不仅考虑了直觉犹豫模糊数间的差异,同时考虑了犹豫度的影响,决策者可以根据对直觉犹豫模糊数和犹豫度之间偏好的不同,设置不同的偏好值得到距离测度。然后基于这些距离测度,又提出了直觉犹豫模糊环境下的TOPSIS法。最后通过实例说明了所提出的TOPSIS法的合理性与实用性。

关键词: 直觉犹豫模糊集, 距离测度, 犹豫度, TOPSIS法