Identification of the Choquet integral parameters in the interaction index domain by means of sparse modeling

The Choquet integral has been used as an aggregation operator in the field of multiple criteria decision aiding. Due to its nonlinear nature, the Choquet integral can model interactions between different criteria, such as synergy and redundancy. However, the identification of the Choquet integral parameters is a challenging problem due to its ill-posed nature, which may lead to non-unique solutions. In recent works, this problem has been addressed by considering regularization terms based on sparsity. In this work, this approach is also considered. However, differently from previous studies, in which the Choquet integral is parametrized by means of a fuzzy measure, we propose a novel identification method which exploits sparsity in a transformed domain known as interaction index representation. We provide a set of numerical experiments to assess the proposed method. As a second contribution of the paper, we conduct an identifiability analysis, in which the aim is to search for conditions that ensure that the identification process leads to unique solutions. This analysis is supported by a set of numerical experiments carried out in different scenarios.