中文摘要：

对于区间值犹豫模糊集在多属性决策、聚类分析、模式识别、人工智能等方面的应用来说，距离及相似度概念起着重要作用。本文通过具体实例说明，区间值犹豫模糊集之间的距离和相似度的原有定义存在不足之处，即原有定义只考虑了犹豫区间左右端点值的差异、而没有比较犹豫区间个数的多少。进而，在区间值犹豫模糊集中引入犹豫度的概念，给出区间值犹豫模糊集的距离及相似度的新定义，经过理论分析阐明了新定义的良好性质，并通过一个实际的多属性决策应用问题说明了改进定义的合理性和有效性。

英文摘要：

Distance and similarity play a important role in multiple criteria decision, document clustering, pattern recognition and artificial intelligence. In this paper, we explain some deficiency of the existing distance and similarity of interval-valued hesitant fuzzy sets by numerical examples and found that it only taken into account the values of interval values but failure to considered the number of hesitant intervals. Thus, we introduced the concept of hesitance degree based on interval-valued hesitant fuzzy sets, moreover, several novel distances and similarity measures between interval-valued hesitant fuzzy sets are developed, in addition, we clarified the new definition of good nature through theoretical analysis. At length, a numerical example about multiple criteria decision is given to illustrate the validity of new distance and similarity.