IEEE Trans Cybern. 2014 Aug;44(8):1328-37. doi: 10.1109/TCYB.2013.2283021. Epub 2013 Oct 23.
In this paper, we explore the ranking methods with hesitant fuzzy preference relations (HFPRs) in the group decision making environments. As basic elements of hesitant fuzzy sets, hesitant fuzzy elements (HFEs) usually have different numbers of possible values. In order to compute or compare HFEs, we have two principles to normalize them, i.e., the α -normalization and the β -normalization. Based on the α -normalization, we develop a new hesitant goal programming model to derive priorities from HFPRs. On the basis of the β -normalization, we develop the consistency measures of HFPRs, establish the consistency thresholds to measure whether or not an HFPR is of acceptable consistency, and then use the hesitant aggregation operators to aggregate preferences in HFPRs to obtain the ranking results.
在本文中，我们探讨了群体决策环境中带有犹豫模糊偏好关系（HFPR）的排序方法。作为犹豫模糊集的基本元素，犹豫模糊元素（HFEs）通常具有不同数量的可能值。为了计算或比较 HFEs，我们有两种归一化它们的原则，即α归一化和β归一化。基于α归一化，我们开发了一种新的犹豫目标规划模型，从 HFPR 中推导出优先级。基于β归一化，我们提出了 HFPR 的一致性度量方法，建立了一致性阈值来衡量 HFPR 是否具有可接受的一致性，然后使用犹豫聚合算子来聚合 HFPR 中的偏好，从而得到排序结果。
