A method for the incorporation of parametric uncertainty in the weighted evaluation multi-attribute decision analysis model

We develop an extension of the classic Weighted Evaluation (WE) Multi-Attribute Decision Analysis (MADA) model that allows for uncertainty in the parameters of the model. Uncertainties in attribute importance weights and alternative evaluation ratings are represented by independent uniform, triangular or beta random variables; and an iterative multi-variate integration scheme is used to evaluate the mean, variance and skewness of the resulting Probabilistic Weighted Evaluation (PWE). These moments are used to compute two-term Edgeworth and normal approximations to the distribution of: (a) the PWE for each of several alternatives that are to be analysed separately; or (b) the difference between PWEs for selected alternatives that are to be analysed on a pairwise basis. The proposed methodology is used to compare probabilistically three alternative solutions to the Mexico City Airport Siting Problem of Keeney and Raiffa (Keeney, R. L. and Raiffa, H., Decisions with Multiple Objectives. Wiley, New York, 1976).