Uncertainty and Probabilistic Methods in Multi-Criteria Decision Analysis

Multi-Criteria Decision Analysis (MCDA) is a collection of techniques for choosing optimal decisions when two or more criteria need to be taken into account in the decision process. Most MCDA techniques require the specification of a number of parameters; criteria weights, utility functions or indifference thresholds. We wish to account for the uncertainty in these parameters which may arise due to the fuzzy nature of the Decision Maker's preferences, conflicting opinions between a group of decision makers or population group, or the abstract nature of the parameters. We implement some MCDA models from a Bayesian perspective where parameters come from posterior probability distributions representing the combination of available knowledge on the parameters. Such knowledge can come from empirical data, expert elicitation, survey data, decision-making committees, or some combination of these. Depending on the method used, the end result is either a benefit function which quantifies the uncertainty in the benefit score for each action, or a rankogram which depicts the uncertainty in the ranking of actions. Knowledge about this uncertainty allows decision makers to make more informed decisions. A decision action may be clear when uncertainty is sufficiently low, or it may be necessary to request more information or to refine the decision formulation if uncertainty is high, potentially leading to improved decision-making.