Abstract: Most of the existing consensus models are based on precise opinions and do not consider the direction constraints of adjusting decision makers' opinions. To solve the problem, this article introducesinterval opinions and explores the consensus-reaching problem under the situation ofasymmetric cost from the perspective of optimization adjustment cost. Firstly, an asymmetric minimum cost consensus model is constructed based on interval opinions. Then, considering the actual needs of decision makers for different levels of consensus, a decision-maker weight allocation method based on the length of the interval opinion is proposed by introducing the soft consensus measures, and an asymmetric minimum cost soft consensus model based on the interval opinion is constructed accordingly. Finally, the effectiveness of the model is verified through an example of the decision-making on pollution reduction between the government and polluters, and then a sensitivity analysis and comparative study are conducted. The results show that: (1)Compared with the precise opinions, using interval opinions can reduce the consensus cost; (2)Compared with the symmetric cost, the total consensus cost considering the asymmetric adjustment cost will not increase indefinitely as the unit adjustment cost increases.

Key words: consensus decision-making, asymmetric cost, interval opinion, minimum cost, soft consensus, weight distribution

摘要： 针对已有共识模型大多是基于精确意见且未考虑决策者意见调整方向约束的不足,引入区间型意见,从最优化角度研究了非对称调整成本下的群决策共识模型。首先,基于区间意见构建了非对称最小成本共识模型。其次,考虑到决策者对不同共识水平的实际需求,通过引入软共识测度,提出了基于区间长度的决策者权重分配方法,据此构建了基于区间意见的非对称最小成本软共识模型。最后,通过政府与污染企业之间关于污染减排决策的实例验证了模型的有效性,并进行了灵敏度分析与比较研究。结果表明:(1)同精确值信息相比,区间意见能够缩减共识成本;(2)与对称成本共识模型相比,非对称调整成本的总共识成本不会随着单位调整成本的增加而无限增大。

关键词: 共识决策, 非对称成本, 区间型意见, 最小成本, 软共识, 权重分配