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...

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...

Most complex scheduling problems are combinatorial problems and difficult to solve. That is why, several methods focus on the optimization according to a single criterion such as makespan, workloads of machines, waiting times, etc. In this paper, the Choquet integral is introduced as a general tool for dealing with multiple criteria decision making and used in optimization flexible job-shop sch...

The outbreak of epidemic has had a big impact on the investment market China. Facing turbulence in market, many enterprises find it difficult to judge development prospects projects and make right decisions. three-way decisions offer novel study perspective solve this problem. Then developed model is applied select projects. Firstly, some relevant attributes project are described with double hi...

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...

Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. However, the commonly used integral condition for almost seconddegree stochastic dominance does not map into the corresponding classes of increasing concave utility functions with bounded der...

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.

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...