OWA aggregation of multi-criteria with mixed uncertain satisfactions

We discuss the Ordered Weighted Averaging (OWA) operator and its role in multi-criteria decision-making. We look at the situation where there is uncertainty in the criteria satisfactions. To allow for various types of uncertainty we assume a measure representation of the uncertain information. Since the OWA aggregation requires an ordering of the arguments we introduce the idea of measure based dominance over the uncertain arguments to provide a mechanism for obtaining this ordering. As we can't always satisfy the strong conditions needed for obtaining a complete dominance relationship over the uncertain arguments in the criteria aggregation we introduce a surrogate for measure-based dominance that can always be calculated. We provide an illustrative example of the whole procedure.