In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski’s and Chebyshev’s type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed in...

A new solution concept: acceptable payoffs in the core via coalition formation Katsushige Fujimoto Inequalities for Choquet integral with respect to a submodular non additive measure Yasuo Narukawa, Vicenç Torra

We propose a general notion of capacity defined on any finite distributive lattice, encompassing usual capacities, bi-capacities, and their immediate extensions called k-ary capacities. We define key notions such as Möbius transform, derivative, Shapley value and Choquet integral.

Our main goal is to extend the domain of a monotone measure to a class of intuitionistic fuzzy sets. The extension is made by using of the Choquet integral.

Given a real valued random variable Θ we consider Borel measures μ on B(R), which satisfy the inequality μ(B) ≥ Eμ(B−Θ) (B ∈ B(R)) (or the integral inequality μ(B) ≥ R∞ −∞ μ(B−h)γ(dh)). We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.

In this paper, we propose a generalization of logistic regression based on the Choquet integral. The basic idea of our approach, referred to as choquistic regression, is to replace the linear function of predictor variables, which is commonly used in logistic regression to model the log odds of the positive class, by the Choquet integral. Thus, it becomes possible to capture non-linear dependen...