Multi-objective stochastic programming problems correspond to economic situations in which economic process is simultaneously influenced by a random environment and a decision parameter selected with respect to multi-objective optimization problem depending on the probability measure. In applications very often the actual probability measure is a little pertubed, has to be replaced by empirical one or for numerical reasons has to be approximated by a simpler one. Consequently, two multi-objective stochastic optimizaion problems (real and approximative) correspond to the original situaion. The aim of the grant project is to focus on the investigation of the relationship between them, especially in the cases of the stochastic dominance constraints, probability constraints and rather general objectives (including nonlinear dopendence on the measure).