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The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions
P. 31–38.
Bronevich A., Rozenberg I.
The aim of this paper is to show that the Kantorovich problem, well known in models of economics and very intensively studied in probability theory in recent years, can be viewed as the basis of some constructions in the theory of belief functions. We demonstrate this by analyzing specialization relation for finitely defined belief functions and belief functions defined on reals. In addition, for such belief functions, we consider the Wasserstein metric and study its connections to disjunctions of belief functions.
In book
Vol. 11069. , Springer, 2018.
Bronevich A., Lepskiy A., International Journal of Approximate Reasoning 2026 Vol. 190 Article 109597
In the paper, we consider three possible types of external conflict in Dempster-Shafer theory and propose its measurement based on functionals evaluating intersection, inclusion and distance between random sets. All proposed functionals can be viewed as extensions of known functionals like Jaccard metric, Jaccard index, and Dice coefficient from usual sets to random sets based ...
Added: February 25, 2026
Арженовский И. В., Региональная экономика и управление: электронный научный журнал 2021 № 3 (67) Статья 11
At the present stage, regional specializations are being formed in the framework of the next technological wave, which is characterized by digitalization, “green” economy, bio- and nanotechnology, knowledge-based economy, and growing attention to human capital. The changes resulting from the Covid-19 pandemic belong to these characteristics as well. The article analyzes the influence of these ...
Added: January 21, 2026
Andrey G. Bronevich, Alexander E. Lepskiy, International Journal of Approximate Reasoning 2025 Vol. 187 Article 109572
In this paper, we extend the ideas of measuring conflict among belief functions based on solving Kantorovich problems to the case of measuring conflict within a belief function. We consider three possible interpretations of conflict-free information and propose the functionals for measuring conflict, which can be considered as counterparts of known functionals like the auto-conflict ...
Added: October 13, 2025
Яковлева П. Э., Смирнова Ю. Д., Общество и экономика 2025 № 3 С. 48–60
The article presents the results of an assessment of the socio-economic development of the single-industry “satellite city” of the nuclear power plant Udomlya with single industry towns similar in population size from the group with a stable socio-economic situation: a tourist town – Sol-Iletsk, another single-industry town Kotovsk and a textile town Furmanov. The assessment ...
Added: September 4, 2025
Popova S., International Mathematics Research Notices 2024 Vol. 2024 No. 18 P. 12645–12662
We study optimal transportation problems with constraints on densities of transport plans. We obtain a sharp condition for the uniqueness of an optimal solution to the Kantorovich problem with density constraints, namely that the Borel measurable cost function h(x, y) satisfies the following non-degeneracy condition: h(x, y) can not be expressed as a sum of functions u(x) ...
Added: November 19, 2024
Khodachek A. M., Инновации 2023 Т. 293 № 3 С. 23–27
Interest in the problems of agglomerations is associated with the emergence of new processes in the development of large urban systems. In the context of the crisis and the growing sanctions regime, this problem is becoming a priority given the new territorial policy being pursued in the Russian Federation, which involves the formation of self-sufficient ...
Added: February 8, 2024
Sergey S. Ketkov, European Journal of Operational Research 2024 Vol. 313 No. 2 P. 602–615
This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in ...
Added: October 31, 2023
Popova S., / Series arXiv "math". 2023.
We consider Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge mappings continuous with respect to the parameter. ...
Added: September 13, 2023
Karavaeva Y., Правоведение 2022 Т. 66 № 1 С. 69–79
Special norms in the criminal law, as a rule, are designed to solve the problem of differentiation of responsibility, so they must contain such features of the composition that significantly change the typical degree of public danger of the act and (or) the figure. These norms are constructed using the casuistic method, which is due ...
Added: October 4, 2022
Han J., Lee K., Economic Modelling 2022 Vol. 112 Article 105853
Many middle-income countries are caught in the middle-income trap, facing a slowdown in growth. Although they are undergoing a structural transformation from labor-intensive to capital-intensive sectors, existing literature does not provide theoretical guidance on which capital-intensive sectors to enter first. This study builds on Schumpeterian sectoral heterogeneity to develop a two sector, two country trade ...
Added: September 12, 2022
Measures of conflict, basic axioms and their application to the clusterization of a body of evidence
Andrey G. Bronevich, Alexander E. Lepskiy, Fuzzy Sets and Systems 2022 Vol. 446 P. 277–300
There are several approaches for evaluating conflict within belief functions. In this paper, we develop one of them based on axioms and show its connections to the decomposition approach. We describe a class of conflict measures satisfying this system of axioms and show that measuring conflict can be realized through the clusterization of a body ...
Added: August 27, 2022
Bogachev V., Резбаев А. В., Математические заметки 2022 Т. 112 № 3 С. 360–370
We study the existence of solutions of Kantorovich problem
where cost function depends on transport plan.
We then consider the case of the cost function depending on
the conditional measures of transport plan.
A wide sufficient conditions for the existence of optimal plans
for Radon marginal distributions are obtained on completely regular spaces
and a lower semicontinuous cost function. ...
Added: June 24, 2022
Dominiak A., Eichberger J. T., Games and Economic Behavior 2021 Vol. 128 P. 125–159
We propose a new solution concept, called Context-Dependent Equilibrium Under Ambi- guity (CD-EUA), for strategic games where players’ beliefs may be influenced by exogenous context-related information. Players’ beliefs about the strategic behavior of their opponents are represented by belief functions. The notion of belief functions allows us to combine ex- ogenous context information in the spirit ...
Added: October 31, 2021
Jürgen Eichberger, Pasichnichenko I., Journal of Economic Theory 2021 Vol. 198 Article 105369
In this paper, we study choice under uncertainty with belief functions. Belief functions can capture par- tial information by describing what is objectively known about the probabilities of events. State-contingent acts together with a belief function over states induce belief functions over outcomes. We assume that de- cision makers have preferences over belief functions that ...
Added: October 31, 2021