We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet integral includes weighted arithmetic means, ordered weighted averaging functions, and lattice polynomial functions as particular cases, our results encompass the corresponding results for these aggregatio...

This paper proposes a new nonlinear classifier based on a generalized Choquet integral with signed fuzzy measures to enhance the classification accuracy and power by capturing all possible interactions among two or more attributes. This generalized approach was developed to address unsolved Choquet-integral classification issues such as allowing for flexible location of projection lines in n-di...

Bi-capacities have been presented recently by the authors as a natural generalization of capacities (fuzzy measures). Usual concepts as Möbius transform, Shapley value and interaction index, Choquet integral, kadditivity can be generalized. We present formulas of the Choquet integral w.r.t. the Möbius transform, and w.r.t. the interaction index for 2-additive bi-capacities.

Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorf...

We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the Möbius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bicapacities are introduced. It is shown that symmetric and asymmetric integrals are recover...

We propose to extend the aggregation scheme of Saaty’s AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the consistency case....

In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng’s g-expectation. An open question has been, after making suitable restrictions to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficien...

In this article we consider the conformal decomposition of Einstein’s constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we combine a priori estimates for the individual Hamiltonian and momentum constraints, barrier constructions...

This paper characterizes properties of chance attitudes (nonadditive measures). It does so for decision under uncertainty (unknown probabilities), where it assumes Choquet expected utility, and for decision under risk (known probabilities), where it assumes rank-dependent utility. It analyzes chance attitude independently from utility. All preference conditions concern simple violations of the ...