In this paper, we address the problem of comparing the performances of two popular aggregation operators, the weighted sum and the Choquet integral, for selecting the best alternative among a set of alternatives, all evaluated according to different criteria. While the weighted sum is simple to use and very popular, the Choquet integral is still hard to use in practice but leads theoretically t...

Fuzzy measures were introduced by M Sugeno in in order to express a grade of fuzziness in the same way that probability measures express a grade of random ness The Sugeno fuzzy integrals are the functionals with monotonicity de ned by using fuzzy measures Later on Murofushi and Sugeno proposed another type of fuzzy integral the Choquet integral based on the Capacity Theory developed by G Choque...

We study the notion of conditional relative importance in a quantitative framework. This is an important notion in the context of the Choquet integral since this latter is usually motivated by this decisional behavior. A systematic investigation on generalizations of the Choquet integral is performed. The determination of the utility function is central in this analysis.

In this paper we discuss the Choquet integral model in the realm of Preference Learning, and point out advantages of learning simultaneously partial utility functions and capacities rather than sequentially, i.e., first utility functions and then capacities or vice-versa. Moreover, we present possible interpretations of the Choquet integral model in Preference Learning based on Shapley values a...

We propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also called Šipoš integral. Our framework is purely ordinal, since the Sugeno integral has its interest when the underlying structure is ordinal. We begin by defining negative numbers on a linearly ordered set, and we endow this new structure with a suitable algebra...

Every invariant biseparable preference relation can be represented by an integral on the set of continous a¢ ne mappings over a set of priors, where the integral is taken in the sense of Choquet. In looser terms: the representation takes the form of an integration over priors. As a by-product, we provide a novel interpretation of the (f)-MEU functional and of its relation with the Choquet integ...

Following the ideas of the axiomatic characterization of the Choquet integral due to [D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986) 255–261] and of the Sugeno integral given in [J.-L. Marichal, An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Trans. Fuzzy Syst. 9 (2001...

We consider a collection F of subsets of a finite set N together with a capacity v : F → R+ and call a function f : N → R measurable if its level sets belong to F . Only in this case, the classical definition of the Choquet integral works in our wider context. In this article, we provide a general framework for a Choquet integral that works also for non-measurable functions f and includes the i...

In this paper we show how the distribution of the discrete Choquet integral can be analytically computed. The advantage of having an analytical expression is that the value of the cumulative distribution function (cdf) can be computed exactly for the Choquet. We also derive an expression for the density of the Ordered Weighted Average (OWA) operator, which is a special case of the Choquet.

Keywords: Monotone measure Atom Weak null-additivity Regularity Sugeno integral Choquet integral a b s t r a c t In this paper, we prove some properties of atoms of weakly null-additive monotone measures. By using the regularity and weak null-additivity, a sin-gleton characterization of atoms of monotone measures on a metric space is shown. It is a generalization of previous results obtained by...