An unsupervised capacity identification approach based on Sobol' indices

TL;DR

This paper introduces an unsupervised method using Sobol' indices to identify capacities in aggregation models, aiming to reduce bias from correlated criteria in ranking problems.

Contribution

It proposes a novel unsupervised approach for capacity estimation in multilinear models, addressing the challenge of bias due to criterion correlations without requiring decision maker preferences.

Findings

Method effectively mitigates bias from correlated criteria.

Numerical experiments validate the approach on synthetic data.

Provides a fairer aggregation in ranking tasks.

Abstract

In many ranking problems, some particular aspects of the addressed situation should be taken into account in the aggregation process. An example is the presence of correlations between criteria, which may introduce bias in the derived ranking. In these cases, aggregation functions based on a capacity may be used to overcome this inconvenience, such as the Choquet integral or the multilinear model. The adoption of such strategies requires a stage to estimate the parameters of these aggregation operators. This task may be difficult in situations in which we do not have either further information about these parameters or preferences given by the decision maker. Therefore, the aim of this paper is to deal with such situations through an unsupervised approach for capacity identification based on the multilinear model. Our goal is to estimate a capacity that can mitigate the bias introduced by correlations in the decision data and, therefore, to provide a fairer result. The viability of our proposal is attested by numerical experiments with synthetic data