Bayesian best-worst method: A probabilistic group decision making model

Abstract

The best-worst method (BWM) is a multi-criteria decision-making method which finds the optimal weights of a set of criteria based on the preferences of only one decision-maker (DM) (or evaluator). However, it cannot amalgamate the preferences of multiple decision-makers/evaluators in the so-called group decision-making problem. A typical way of aggregating the preferences of multiple DMs is to use the average operator, e.g., arithmetic or geometric mean. However, averages are sensitive to outliers and provide restricted information regarding the overall preferences of all DMs. In this paper, a Bayesian BWM is introduced to find the aggregated final weights of criteria for a group of DMs at once. To this end, the BWM framework is meaningfully viewed from a probabilistic angle, and a Bayesian hierarchical model is tailored to compute the weights in the presence of a group of DMs. We further introduce a new ranking scheme for decision criteria, called credal ranking, where a confidence level is assigned to measure the extent to which a group of DMs prefers one criterion over one another. A weighted directed graph visualizes the credal ranking based on which the interrelation of criteria and confidences are merely understood. The numerical example validates the results obtained by the Bayesian BWM while it yields much more information in comparison to that of the original BWM.