In this paper, we introduce a kernel for monotone data derived from the Choquet integral with its underlying fuzzy measure. While a naïve computation of this kernel has a complexity that is exponential in the number of data attributes, we propose a more efficient approach with quadratic time complexity. Kernel PCA and SVM classification are employed to illustrate characteristics and benefits of...

The Shilkret integral is maxitive (i.e., the integral of a pointwise supremum of functions is the supremum of their integrals), but defined only for nonnegative functions. In the present paper, some properties of this integral (such as subadditivity and a law of iterated expectations) are studied, in comparison with the additive and Choquet integrals. Furthermore, the definition of a maxitive i...

Linear digital signal processing consists in convoluting the input sampled signal with the discrete version of the impulse response of a filter designed by an expert. More than often, a unique impulse response does not represent the complete knowledge of the expert who should have proposed more than one appropriate filter. In a recent paper, we have proposed an extension of the finite impulse r...

This paper characterizes the core of a differentiable convex distortion of a probability measure on a non atomic space by identifying it with the set of densities which dominate the derivative of the distortion, for second order stochastic dominance. Furthermore the densities that have the same distribution as the derivative of the distortion are the extreme points of the core. These results ar...

A general procedure for extending finite-dimensional "additive-like" representations for binary relations to infinite-dimensional "integral-like" representations is developed by means of a condition called truncation-continuity. The restriction of boundedness of utility, met throughout the literature, can now be dispensed with, and for instance normal distributions, or any other distribution wi...