Supervised learning to aggregate data with the Sugeno integral

The problem of learning symmetric capacities (or fuzzy measures) from data is investigated toward applications in data analysis and prediction as well as decision making. Theoretical results regarding the solution minimizing the mean absolute error are exploited to develop an exact branch-refine-and-bound-type algorithm for fitting Sugeno integrals (weighted lattice polynomial functions, max-min operators) with respect to symmetric capacities. The proposed method turns out to be particularly suitable for acting on ordinal data. In addition to providing a model that can be used for the general data regression task, the results can be used, among others, to calibrate generalized h-indices to bibliometric data.