Abstract: 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.

Key words: grey group off-target deviation degree, grey target decision, grey numbers, regret theory, optimal weight