The idea of using the Choquet integral as an aggregation operator in machine learning has gained increasing attention in recent years, and a number of corresponding methods have already been proposed. Complementing these contributions from a more theoretical perspective, this paper addresses the following question: What is the VC dimension of the (discrete) Choquet integral when being used as a...

In this paper we introduce the semi-uninorm based ordered weighted averaging (SUOWA) operators, a new class of aggregation functions that, as WOWA operators, simultaneously generalize weighted means and OWA operators. To do this we take into account that weighted means and OWA operators are particular cases of Choquet integral. So, SUOWA operators are Choquet integral-based operators where thei...

This chapter of a collective book aims at presenting cardinal extensions of the EU model, based on the Choquet integral, which allow to take into account observed behaviors as in Allais’ paradox under risk or Ellsberg’s paradox under uncertainty, where the expected utility model is violated. Under a key axiom, the comonotonic independence axiom,Schmeidler under uncertainty, and Quiggin and Yaar...

and key words After a general introduction on multicriteria decision aid, we briefly present the two main approaches (outranking methods, multi-attribute utility). Then we focus on the multi-attribute utility framework, which we build in a new perspective, based on the MACBETH methodology and the notion of capacity. We show that the Choquet integral appears as a natural tool for aggregating cri...

In this paper, we review two of the most well-known citation indexes and establish their connections with the Choquet and Sugeno integrals. In particular, we show that the recently established -index is a particular case of the Sugeno integral, and that the number of citations corresponds to the Choquet integral. In both cases, they use the same fuzzy measure. The results presented here permit ...

The paper presents and discusses a method for rank-ordering alternatives on the basis of constraints induced by generic principles (expressing for instance the relative importance of criteria), or by examples of orderings between particular alternatives, without resorting to the use of an aggregation operation for evaluating the alternatives. The approach, which remains qualitative, is based on...

The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic duality between bases and invertible linear transform (e.g., the Möbius transfo...

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 [3] we introduced a “monotone-type” (that is, Choquet-type) integral for realvalued functions, with respect to finitely additive positive set functions, with values in a Dedekind complete Riesz space. A “Lebesgue-type” integral for such kind of functions was investigated in [7]. In [4] we gave some comparison results for these types of integrals. In [10], a Choquet-type integral for real-val...