Inducing a probability distribution in Stochastic Multicriteria Acceptability Analysis

TL;DR

This paper introduces methods to construct probability distributions over value functions in stochastic multicriteria decision analysis, enhancing the statistical interpretation of preferences with extensive simulations and sensitivity analysis.

Contribution

It proposes novel methods to induce probability distributions on value functions based on decision maker preferences, improving the robustness of stochastic multicriteria acceptability analysis.

Findings

Methods successfully induce probability distributions aligning with preferences.

Simulation results validate the effectiveness of the proposed approaches.

Sensitivity analysis demonstrates robustness of the methods.

Abstract

In multiple criteria decision aiding, very often the alternatives are compared by means of a value function compatible with the preferences expressed by the Decision Maker. The problem is that, in general, there is a plurality of compatible value functions, and providing a final recommendation on the problem at hand considering only one of them could be considered arbitrary to some extent. For such a reason, Stochastic Multicriteria Acceptability Analysis gives information in statistical terms by taking into account a sample of models compatible with the provided preferences. These statistics are given assuming the existence of a probability distribution in the space of value functions being defined a priori. In this paper, we propose some methods aiming to build a probability distribution on the space of value functions considering the preference information given by the Decision Maker. To prove the goodness of our proposal we performed an extensive set of simulations. Moreover, a sensitivity analysis on the variables of our procedure has been done as well.