Parameter learning and applications of the inclusion-exclusion integral for data fusion and analysis

© 2019 Elsevier B.V. Developments in the learning and interpretation of fuzzy integrals have paved the way for a myriad of applications in data analysis and prediction. The ability of the associated fuzzy measure to model heterogeneous interactions allow high flexibility when it comes to data fusion tasks – comparable to that of neural networks – however the fuzzy integral structure and properties also afford a degree of robustness and interpretability not enjoyed by such tools. On the other hand, neural network architectures can accommodate fuzzy integrals as a special case. In this paper, we propose that such a representation allows us to naturally extend and adapt the fuzzy integral framework toward specific applications. We focus on the inclusion-exclusion integral, which is a generalization of the Choquet integral, and detail methods for learning the various parameters, given its extended architecture. We then validate the performance and usefulness of this approach on some benchmark datasets.