A Method of Risky Multi-objective Group Decision-Making

The multi-objective group decision-making problem under risk is common in reality. This paper focuses on risky this problem where the objective value is not certain employing fuzzy set theory. We give objectives classifying method and objective normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, then the optimal membership degree of every decision-maker to every alternative can be obtained, and By building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, then the optimal membership degree of every decision-maker to every alternative can be obtained, which are based on both probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and approach for solving multi-objective decision-making Problem among uncertain system, which is applicable for practical problem. Finally a case study showed a satisfactory result.