We consider the multiattribute decision-making problem under risk with partial information of the decision-makers' preferences modelled through an imprecise vectorial utility function and where the consequences are assumed under uncertainty. In this framework under imprecision, we introduce the appropriate utility efficient set that plays a fundamental role because it is where the decision-maker must look for a solution. However, this set can be difficult to determine. So, we provide a decision support system with a solution strategy based on interactive simulated annealing for generating a subset of efficient solutions that gives a fair representation of the whole set, to progressively derive one or several satisfying solutions to aid the decision-maker in his/her final choice.