Related papers: Choquet operators associated to vector capacities
In this paper, we propose a new generalization of the classical discrete Choquet integral to the multivalued framework in terms of an admissible order that refines the natural partial order on the considered value set. The new Choquet-like…
In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…
Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize Integral operators (in the sense of…
The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way,…
A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…
The main aim of this paper is to show that the nonlinear Choquet integral can be used to construct nonlinear approximation operators, exactly as by the use in probability of the Lebesgue-type integral, linear and positive approximation…
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can…
We consider inequalities where integrals are defined in the sense of Choquet with respect to Hausdorff content. We study cases where continuously differentiable functions are defined on open, connected sets with so much regularity that…
As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, Choquet decompositions and Choquet convex decompositions, as well as their corresponding hull operators…
We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
Based on a study of a formula representing submodular set function as a supremum of measures dominated by the set function, we present a corresponding formula for a Choquet integration with respect to the set function, on a measurable space…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
We show that every operator system (and hence every unital operator algebra) has sufficiently many boundary representations to generate the C*-envelope.
In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive semidefinite operator ?, is defined in terms of the d2 coherent states in this system. The Choquet integral CQ of the Q-function, is introduced…
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
We introduce a~\textit{Choquet-Sugeno-like operator} generalizing many operators for bounded functions and monotone measures from the literature, e.g., Sugeno-like operator, Lov\'{a}sz and Owen measure extensions, $\rF$-decomposition…
We aim at representing the recently introduced conditional aggregation-based Choquet integral as a standard Choquet integral on a hyperset. The representation is one of transformations considered by R.R. Yager and R. Mesiar in 2015. Thus we…
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…
In this paper we study to what extend some properties of the classical linear Volterra operators could be transferred to the nonlinear Volterra-Choquet operators, obtained by replacing the classical linear integral with respect to the…