Abstract: For the hesitant fuzzy linguistic information Multi-Attribute Decision Making（MADM） problems, based on the hesitant fuzzy linguistic possibility degree, a linear assignment decision making model is developed. Firstly, with the envelope transformation method of Hesitant Fuzzy Linguistic Element（HFLE）, the concepts of possibility degree and relative difference index between the HFLE are introduced. Then, some properties are discussed, in which the possibility degree matrix and relative difference matrix are fuzzy complementary judgment matrices, and the optimal degree of HFLE is constructed. In the end, under the hesitant fuzzy linguistic environment, a novel linear assignment decision making model is proposed to determine the collected optimal degree of alternatives, and the most desirable alternative is selected. The numerical example shows that the rationality and effectiveness of the developed model.

Key words: hesitant fuzzy linguistic set, possibility degree, relative difference index, optimal degree, linear assignment model

摘要： 针对属性值为犹豫模糊语言元的多属性决策问题，建立基于犹豫模糊语言可能度的线性分配决策模型。首先，基于犹豫模糊语言元的包络转化方法，分别定义了犹豫模糊语言元间的可能度和相对差异指数等概念；其次探究发现可能度矩阵和相对差异矩阵均为互补判断矩阵，并设计了犹豫模糊语言元的最优度计算公式；最后，在犹豫模糊语言信息环境下，构建了一种新的线性分配决策模型用以确定各备选方案的综合最优度，进而遴选出最优方案。实验结果表明，提出的决策模型是可行和有效的。

关键词: 犹豫模糊语言集, 可能度, 相对差异指数, 最优度, 线性分配模型