Robust fitting for the Sugeno integral with respect to general fuzzy measures

Abstract

The Sugeno integral is an expressive aggregation function with potential applications across a range of decision contexts. Its calculation requires only the lattice minimum and maximum operations, making it particularly suited to ordinal data and robust to scale transformations. However, for practical use in data analysis and prediction, we require efficient methods for learning the associated fuzzy measure. While such methods are well developed for the Choquet integral, the fitting problem is more difficult for the Sugeno integral because it is not amenable to being expressed as a linear combination of weights, and more generally due to plateaus and non-differentiability in the objective function. Previous research has hence focused on heuristic approaches or simplified fuzzy measures. Here we show that the problem of fitting the Sugeno integral to data such that the maximum absolute error is minimized can be solved using an efficient bilevel program. This method can be incorporated into algorithms that learn fuzzy measures with the aim of minimizing the median residual. This equips us with tools that make the Sugeno integral a feasible option in robust data regression and analysis. We provide experimental comparison with a genetic algorithms approach and an example in data analysis.