We introduce mixed integer linear programming under preference uncertainty, a novel approach for supporting decision-making when the decision-maker’s preferences are uncertain. Here, each feasible design is associated with a vector of attributes, and each vector is assigned a utility through the decision-maker’s utility function, which has been incompletely estimated through preference learning, and whose remaining uncertainty is quantified by a Bayesian prior or posterior probability distribution. We develop new optimization-based algorithms with theoretical guarantees that provide a menu of diverse solutions among which the decision maker is likely to find a solution that performs well according to her preferences.