For the qualitative results of pointwise and uniform approximation obtained in [10], we present general quantitative estimates in terms of the modulus of continuity and in terms of a K-functional, for the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x , written in terms of the Choquet integral with respect to a family of monotone and submodular set functions, Γn,x, on the standar...

Fuzzy measures and integrals have been used in multiple applications in the area of information fusion. They can be used to aggregate information when information sources are not independent. Fuzzy measures are used to represent our background knowledge on the information sources. In particular, they can be used to model the dependencies between the variables. One of the applications of Choquet...

In this paper, we introduce the Choquet integral as a general tool for dealing with multiple criteria decision making. After a theoretical exposition giving the fundamental basis of the methodology, practical problems are addressed, in particular the problem of determining the fuzzy measure. We give an example of application, with two different approaches, together with their comparison.

Let (Ω, d) be a metric space where Ω is a set with positive and finite Hausdorff outer measure in its Hausdorff dimension and let B be a partition of Ω. The coherent upper conditional prevision defined as the Choquet integral with respect to its associated Hausdorff outer measure is proven to satisfy the disintegration property and the conglomerative principle on every partition.

The aim of this paper is to show how fuzzy measures and intervals can be combined in order to provide a simple and accurate practical solution to multi-criteria decision making problems. More specifically, we construct an interval-based Choquet integral in order to derive preferences over a set of multidimensional alternatives.

In the last few decades the Choquet integral and the Sugeno integral have had several applications in many fields of mathematics, soft computing, pattern recognition and decision analysis [4, 5, 7, 17, 21]. It shows up in the recently published papers that some new types of integrals on symmetric scales are useful tools for applications in decision making problems [6, 8, 12, 21]. The Sugeno int...

This paper deals with decision making under uncertainty when the worth of acts is evaluated by means of Sugeno integral. One limitation of this approach is the coarse ranking of acts it produces. In order to refine this ordering, a mapping from the common qualitative utility and uncertainty scale to the reals is proposed, whereby Sugeno integral is changed into a Choquet integral. This work rel...