Bayesian Weighting for Multiple Criteria Group Decision-Making With Interval Preference Information

Abstract

In multiple criteria group decision-making (MCGDM), decision-making results are influenced by the preferences of decision-makers (DMs) and the accuracy of decision information. Existing studies rarely considered the psychological factors of DMs and the imprecise information of criteria importance when aggregating group opinions. This article proposes a robust MCGDM method that aggregates group opinions incorporating psychological factors of DMs and criteria weights determined by an interval information-based Bayesian hierarchy best worst method. First, a programming model, with an objective of minimizing the difference between the original and adjusted opinions of DMs, is developed to objectively determine the weights of DMs, taking into account the tolerance levels of DMs for opinion adjustments. Additionally, considering the interval preference information of criteria importance, a Bayesian hierarchy best worst method is proposed to infer the probability distribution of criteria weights, in which the criteria weights are regarded as stochastic variables. A numerical example shows that ignoring psychological factors of DMs can lead to biased decisions, while the proposed method providing a probabilistic distribution of alternative rankings forms robust decision results.