Unified Bayesian Frameworks for Multi-criteria Decision-making Problems

TL;DR

This paper presents Bayesian probabilistic frameworks for multi-criteria decision-making that handle uncertainty, group preferences, and criteria correlation, validated through numerical experiments demonstrating their effectiveness.

Contribution

It introduces novel Bayesian models for MCDM that incorporate uncertainty, group decision analysis, and probabilistic ranking, advancing the methodological toolkit.

Findings

Effective handling of preference uncertainty with Bayesian models

Identification of homogeneous decision-maker subgroups

Improved criteria and alternative ranking accuracy

Abstract

This paper introduces Bayesian frameworks for tackling various aspects of multi-criteria decision-making (MCDM) problems, leveraging a probabilistic interpretation of MCDM methods and challenges. By harnessing the flexibility of Bayesian models, the proposed frameworks offer statistically elegant solutions to key challenges in MCDM, such as group decision-making problems and criteria correlation. Additionally, these models can accommodate diverse forms of uncertainty in decision makers' (DMs) preferences, including normal and triangular distributions, as well as interval preferences. To address large-scale group MCDM scenarios, a probabilistic mixture model is developed, enabling the identification of homogeneous subgroups of DMs. Furthermore, a probabilistic ranking scheme is devised to assess the relative importance of criteria and alternatives based on DM(s) preferences. Through experimentation on various numerical examples, the proposed frameworks are validated, demonstrating their effectiveness and highlighting their distinguishing features in comparison to alternative methods.