属性权重未知情况下犹豫模糊多属性决策方法

针对属性权重未知的犹豫模糊多属性决策，利用犹豫模糊元边界的确定性与边界内隶属度的犹豫性，把犹豫模糊元转换成集对分析中的三元联系数；再根据三元联系数的势函数和属性离差最大法确定属性权重，基此建立属性权重未知条件下的基于三元联系数的犹豫模糊多属性决策模型，利用模型中不同犹豫强度对备选方案进行排序。实例计算和对比分析结果表明，新模型不仅包含了其他模型得到的结果，还提供了更多潜在的排序方案信息，由此形成的有条件决策，是犹豫模糊多属性决策不确定性本质属性的映照，与犹豫模糊多属性决策实际应用情况吻合。

A hesitant fuzzy multi-attribute decision-making method with unknown attribute weights

For hesitant fuzzy multi-attribute decision making (HFMADM) with unknown attribute weight, using the certainty of the hesitation fuzzy element boundary and the hesitation of the membership degree within the boundary, the hesitant fuzzy element is transformed into the ternary connection number (TCN) in set pair analysis. The attribute weight is then determined using the potential function of the TCN and the principle of maximum deviation of attributes. Furthermore, a hesitant fuzzy multi-attribute decision-making model based on TCN is established under the condition of unknown attribute weight. The possible ranking of alternatives is discussed by using different hesitant intensity values in the model. The results of case calculation and comparative analysis show that the new model not only contains the findings of other models but also provides other possible ranking alternatives. The conditional decision formed by this model reflects the essential attribute of uncertainty in HFMADM, which is consistent with its practical application.