考虑后悔规避的灰色群体偏离靶心度决策方法

针对指标值、指标权重以及状态概率均为区间灰数的风险型多指标群决策问题,考虑决策者的后悔规避的心理行为,提出基于后悔理论和区间灰数信息的群体偏离靶心度决策方法。该方法将后悔理论融入到群决策过程中,建立了各决策者的综合灰色感知效用矩阵,由此定义了群体灰色正负靶心以及灰色群体偏离靶心度;以灰色群体偏离靶心度综合值最大化为目标、同时结合极大熵原理构建优化模型并解出最优专家权重向量,利用灰色群体偏离靶心度大小对方案进行排序;最后,通过具体算例验证了该方法的有效性和实用性。

Grey Off-target Deviation Degree Method for Group Decision-making with Regret Aversion

Grey target method plays an important role in solving multi-attribute decision-making problems. Especially in recent years, because of the increasing complexity of the practical decision-making problems, the group grey target method in uncertain environments has attracted more and more attention. Meanwhile, researchers have concluded that the risk attitude and behavior characteristics of decision-makers have a direct impact on decision results. As the most avoidable emotion in decision-making, regret has gradually become the focus of the decision-making field. However, few attempts have been made to incorporate regret theory into the group grey target model. As a result, the off-target deviation degree method based on regret theory is proposed in this paper to solve the problem of risky multi-attribute group decision-making in which the attribute values, attribute weight and state probability are interval grey numbers. In the situation of considering the decision-makers’ psychological behavior with regret aversion, the regret theory is integrated into group decision-making by constructing the grey perceived utility matrix of each decision-maker, and the grey group positive clout and negative clout are defined. Then the grey group off-target deviation degree is also defined, which is denoted as ε_i(⊗). The bigger ε_i(⊗) is, the better the scheme A_i is. An optimal model which produces the maximum comprehensive off-target deviation degree with the maximum entropy is built to get the optimal weight vector of decision-maker, so that the grey group off-target deviation degree of each scheme is ranked. Finally, a case study about the selection of development schemes for a new product is presented to show the method is effective and practical. The approach in this paper makes a model of grey off-target deviation degree for group decision-making with regret aversion on basis of interval grey numbers, which take both the psychological behavior and the uncertainty of real world into account. The model is not only more applicable to the practical problems, but also provides a new way and perspective for group grey target decision making.