In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These are generalization the “standard” Choquet integral obtained by replacing difference in definition usual dissimilarity function. In particular, all integrals encompasses but use dissimilarities provides higher flexibility and generality. We show that some aggregation/pre-aggregation/averaging/fun...

We introduce a measure of entropy for any discrete Choquet capacity and we interpret it in the setting of aggregation by the Choquet integral.

We introduce a Choquet-Sugeno-like operator generalizing many operators for bounded nonnegative functions and monotone measures from the literature, e.g., Sugeno-like operator, Lovász Owen measure extensions, F-decomposition integral with respect to partition decomposition system, others. The new is based on concepts of dependence relation conditional aggregation operators, but it does not depe...

The integral representation of Choquet operators defined on a space C(X) is established by using the Choquet-Bochner real-valued function with respect to vector capacity.

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symm...

In the cumulative prospect theory (CPT) the preference (utility functional) is represented by the difference of two Choquet integrals. We investigate representations of the corresponding functional by two fuzzy integrals, specially the difference representations of the asymmetric Choquet integral with respect to a signed fuzzy measure with bounded chain variation. We discuss non-monotone, real ...

Our purpose in this paper is to show the integration properties of the intuitionistic fuzzyvalued Choquet integrals, by which improper applications of this type of Choquet integral in the multicriteria decision making can be avoided. We first propose some important operational properties of intuitionistic fuzzy values (IFVs) and give a short review of the methods of comparing IFVs in the framew...

Choquet capacities are a generalization of probability measures that arise in robustness, decision theory and game theory. Many capacities that arise in robustness are symmetric or can be transformed into symmetric capacities. We characterize the extreme points of the set of upper distribution functions corresponding to coherent, symmetric Choquet capacities on [0,1]. We also show that the set ...

This note completes the main result of [Zimper A., (2010) Re-examining the law of iterated expectations for Choquet decision makers. Theory and decision, DOI 10.1007/s11238-010-9221-8], by showing that additional conditions are needed in order the law of iterated expectations to hold true for Choquet decision makers. Due to the comonotonic additivity of Choquet expectations, the equation E[f, ν...