Choquet integral has proved to be an effective aggregation model in multiple criteria decision analysis when interactions between criteria have to be taken into consideration. Recently, some generalizations of Choquet integral have been proposed to take into account more complex forms of interaction. This is the case of the bipolar Choquet integral and of the level dependent Choquet integral. T...

We say that a linear subspace A of C0(X) is strongly separating if given any pair of distinct points x1, x2 of the locally compact space X, then there exists f ∈ A such that |f(x1)| 6= |f(x2)|. In this paper we prove that a linear isometry T of A onto such a subspace B of C0(Y ) induces a homeomorphism h between two certain singular subspaces of the Shilov boundaries of B and A, sending the Cho...

Inspired by the interactive discrete choice logit models [Aggarwal, 2019], this paper presents the advanced families of discrete choice models, such as nested logit, mixed logit, and probit models to consider the interaction among the attributes. Besides the DM's attitudinal character is also taken into consideration in the computation of choice probabilities. The proposed choice models make us...

We study in this paper the generation of the Choquet optimal solutions of biobjective combinatorial optimization problems. Choquet optimal solutions are solutions that optimize a Choquet integral. The Choquet integral is used as an aggregation function, presenting di erent parameters, and allowing to take into account the interactions between the objectives. We develop a new property that chara...

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; Φ((C) ∫ fdμ) ≤ (C) ∫ Φ(f)dμ, where f is Choquet integrable, Φ : [0,∞) −→ [0,∞) is convex, Φ(α) ≤ α for all α ∈ [0,∞) and μf (α) ≤ μΦ(f)(α) for all α ∈ [0,∞). Furthermore, we give some examples assuring both satisfaction ...

Résumé : L’utilisation de l’intégrale de Choquet en Aide Multicritère à la Décision (AMCD) nécessite l’identification de la capacité qui lui est associée. Nous proposons ici un algorithme de détermination d’une capacité pour l’intégrale de Choquet 2-additive à partir d’une information ordinale fournie par le décideur. Mots-clés : AMCD, intégrale de Choquet, capacité 2-additive. Abstract: The us...

Expectation is the fundamental concept in statistics and probability. As two generalizations of expectation, Choquet and Choquet-like expectations are commonly used tools in generalized probability theory. This paper considers the Stolarsky inequality for two classes of Choquet-like integrals. The first class generalizes the Choquet expectation and the second class is an extension of the Sugeno...

In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can ...