Study of Manhattan’s consensus degrees through an extension based on the Uniform distribution

The authors would like to acknowledge the Spanish State Research Agency support under the Project PID2019-103880RB-I00/ AEI/10.13039/501100011033.An important aspect to be considered in Group Decision Making problems is the study of consensus. Since in these problems it is desirable that the final decision is widely accepted, improving the consensus degree in a fair way is a very interesting task. This paper analyses the improvement in the consensus degrees -obtained by applying Manhattan distance-when the experts' preferences are slightly modified using one of the properties of the Uniform distribution. We carry out an experimental study that shows the enhancement in different cases to which Uniform extension has been applied, with different number of both, experts and alternatives.Spanish Government PID2019-103880RB-I00/ AEI/10.13039/50110001103

Unified Bayesian Frameworks for Multi-criteria Decision-making Problems

This paper presents Bayesian frameworks for different tasks within multi-criteria decision-making (MCDM) based on a probabilistic interpretation of the MCDM methods and problems. Owing to the flexibility of Bayesian models, the proposed frameworks can address several long-standing and fundamental challenges in MCDM, including group decision-making problems and criteria correlation, in a statistically elegant manner. Also, the models can accommodate different forms of uncertainty in the preferences of the decision makers (DMs), such as normal and triangular distributions as well as interval preferences. Further, a probabilistic mixture model is developed that can group the DMs into several exhaustive classes. A probabilistic ranking scheme is also designed for both criteria and alternatives, where it identifies the extent to which one criterion/alternative is more important than another based on the DM(s) preferences. The experiments validate the outcome of the proposed frameworks on several numerical examples and highlight its salient features compared to other methods