Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker's (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our model is applicable to problems with inconsistent and mutable preference representations which are ubiquitous in practice, particularly in group or social decision making. In the framework of distributionally robust optimization, data-driven approaches are discussed to construct two ambiguity sets of the probability distributions of the DM's preference: one is an ellipsoidal moment region with a sample mean and sample covariance matrix, the other is a nonparametric percentile-t bootsrap confidence region. A numerical example of vehicle design demonstrates the effectiveness of the proposed model working with machine learning methods. We first depict the random preference in the structure of piecewise linear additive multi-attribute utility functions, which are either nondecreasing or risk averse, and next develop tractable reformulations and solution algorithms. Finally we extend to general continuous random utility functions and carry out convergence analysis of the proposed piecewise linear approximation as the size of sample data increases.
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