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

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