Abstract: This paper investigates the interval-valued hesitant fuzzy multiple attribute decision making method with preference relations on attributes based on interval-valued signed distance measure. Firstly, in order to solve the problem of subjectivity caused by adding elements into an interval-valued hesitant fuzzy element, based on the interval-valued hesitant fuzzy information, the concept of improved hesitancy index is given considering the number of elements, and the definition of improved signed distance based on the improved hesitancy index is given. Secondly, an interval-valued hesitancy index with logarithmic function based on the number and variance of interval-valued  elements in interval-valued hesitant fuzzy sets is presented, and an interval-valued hesitant fuzzy signed distance measure based on the interval-valued hesitancy index is proposed. Then, based on the interval-valued signed distance, a mathematical model with preference relations on attributes is given to determine the attribute weights, and the priorities of alternatives can be obtained. Finally, a numerical example shows that the proposed method in this paper is obvious and effective.

Key words: interval-valued hesitant fuzzy sets, interval-valued hesitancy index, interval-valued signed distance, preference relations on attributes, variance

摘要： 针对属性值为区间犹豫模糊元且属性间存在优先级的多属性决策问题，提出一种基于区间犹豫模糊符号距离的多属性决策方法。首先，针对区间犹豫模糊元中人为添加元素导致的主观性过强问题，基于区间犹豫模糊信息给出一种考虑元素个数的改进犹豫度的概念，并在此基础上给出基于区间犹豫模糊信息的改进符号距离的定义；其次，根据区间犹豫模糊集中区间元素之间方差以及区间元素个数定义一种含有对数函数的区间犹豫度，并基于区间犹豫度定义了一种基于区间犹豫模糊信息的区间符号距离；再次，基于该区间符号距离给出一种具有属性优先级的属性权重确定方法，并利用加权符号距离对备选方案进行排序；最后，数值案例显示所提方法可行、有效且区分度明显。

关键词: 区间犹豫模糊集, 区间犹豫度, 区间符号距离, 属性优先级, 方差