Abstract: The multiobjective decision-making problem under risk is common in reality.This paper focuses on the study about risky multiobjective decision-making problem where the objective value is not certain.Risky objectives classifying method and objectives normalizing formula are given.Based on probability theory and fuzzy theory,the alternative relative optimal membership degree is obtained through building objective function that minimizes integrative weighted distance from best and worst alternative.Then the method how to determine objective weight is proposed.This method provides a new idea and approach for solving multiobjective decision-making problem among uncertain system,which is applicable for practical problem.Finally a case study in water resources system showed a satisfactory result.

Key words: multiobjective decision-making, risk, probability, relative optimal membership degree, weight