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This paper deals with decision making under risk with the Weighted Expected Utility (WEU) model, which is a model generalizing expected utility and providing stronger descriptive possibilities. We address the problem of identifying, within a given set of lotteries, a (near-)optimal solution for a given decision maker consistent with the WEU theory. The WEU model is parameterized by two real-valued functions. We propose here a new incremental elicitation procedure to progressively reduce the imprecision about these functions until a robust decision can be made. We also give experimental results showing the practical efficiency of our method.