Holistic Preference Learning with the Choquet Integral

The current approaches to construct a multi-criteria model based on a Choquet integral are split into two separate steps: construct first the utility functions and then the aggregation function. Unfortunately, the decision maker may feel some difficulties in addressing these tricky steps. In this paper, we propose a preference learning algorithm that constructs both the utility functions and the capacity from several preferences or evaluations. The algorithm is based on a fixed-point approach that transforms the global optimization learning problem into two iterative linear problems. Each problem objective is to minimize the number of non-validated learning examples.