On representation of fuzzy measures for learning Choquet and Sugeno integrals

This paper examines the marginal contribution representation of fuzzy measures, used to construct fuzzy measure from empirical data through an optimization process. We show that the number of variables can be drastically reduced, and the constraints simplified by using an alternative representation. This technique makes optimizing fitting criteria more efficient numerically, and allows one to tackle learning problems with higher number of correlated decision criteria.