An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations
提出一种优化方法，在概率不确定语言偏好关系下同时处理个体一致性和群体共识，通过转换函数和优化模型最小化偏好信息损失，并用央企扶贫基金投资项目选择案例验证。
The use of probabilistic uncertain linguistic preference relations (PULPRs) enriches the flexibility of decision makers (DMs) in group decision making (GDM). However, the GDM models under PULPRs are mainly focussed on the consensus reaching process rather than the individual consistent improvement. The goal of this paper is to manage the consistency and consensus in GDM based on PULPRs, and provide a feasible method for minimising the preference information loss by optimisation model. First, according to DMs’ psychological preferences (optimistic, pessimistic, and neutral characteristics), we proposed a conversion function to fit uncertain linguistic terms in PULPRs, which may be transformed into probabilistic linguistic preference relations. Second, to preserve as much as possible the original preference information of DMs, a consensus model based on optimisation is established, which not only obtains the acceptable group consensus but also guarantees that the consistency level of individuals is acceptable. Finally, we validated the proposed method through a case study of an investment project selection for central enterprises’ poverty alleviation fund. The proposed method provides a new way to deal with GDM problems under PULPRs, and help DMs to reach a certain level of consensus on basis of acceptable consistent level of individuals.