Abstract: Hesitant fuzzy set permits the membership degree of an element to a set to be represented by a set of several possible values and is a powerful tool to express the inconsistent preferences of decision makers. A hesitant fuzzy multiple attribute decision making method is proposed to solve the problem which the assessment deviation should not be too large. First, we define hesitancy degree function and consistency index of hesitant fuzzy element; on this basis, an optimization model is constructed based on the maximization of group consistency index. The attribute weight vector can be obtained by solving the optimization model. Then, grey relational analysis method is implemented to rank and select alternatives. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method.

Key words: hesitant fuzzy sets, group consistency, grey relational analysis, multiple attribute decision making

摘要： 犹豫模糊集允许一个元素属于一个集合的隶属度可以是多个不同的值,是表达决策者之间偏好不一致性的有力工具。针对决策者评价偏差不宜过大的问题,提出了一种基于群体一致性的犹豫模糊多属性决策方法。首先, 我们定义了犹豫模糊元的犹豫度函数,进而定义了犹豫模糊元的一致性指数;在此基础上,构建了基于群体一致性指数最大化的权重优化模型,通过求解优化模型可以得到属性的权重向量。然后,运用灰色关联分析法实现对方案的排序和择优。最后,通过实例分析说明了该方法的可行性和有效性。

关键词: 犹豫模糊集, 群体一致性, 灰色关联分析, 多属性决策