Three different types of universal integral based on level dependent capacities are introduced and discussed. Two extremal types are based on Caratheodory’s idea of inner and outer measures, while the third type is introduced for copula-based universal integrals only. Keywords—Choquet integral, Copula, Fuzzy measure, Level dependent capacities, Sugeno integral, Universal integral.

This paper presents a method for solving the multicriteria group decision making problem in an uncertain linguistic environment. To ensure an effective aggregation of the uncertain linguistic variables in multicriteria group decision making for adequately modeling the uncertainty and imprecision of the decision making process, an uncertain linguistic Choquet integral operator is proposed. A met...

We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lovász extension, when regarded as a real function of a random sample drawn from a continuous population. Since the Choquet integral includes weighted arithmetic means, ordered weighted averaging operators, and lattice polynomials as particular cases, our results encompass the correspo...

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...

This paper is devoted to the search of Choquet-optimal solutions in finite graph problems with multiple objectives. The Choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives. We first present a condition on preferences (name hereafter preference for interior points) that characterizes preferences favouring ...