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Conjunctive rules in the theory of belief functions and their justification through decisions models.
P. 137–145.
Andrey G. Bronevich, Rozenberg I.
In the paper we argue that aggregation rules in the theory of belief functions should be in accordance with underlying decision models, i.e. aggregation produced in conjunctive manner has to produce the order embedded to the union of partial orders constructed in each source of information; and if we take models based on imprecise probabilities, then such aggregation exists if the intersection of underlying credal sets is not empty. In the opposite case there is contradiction in information and the justifiable functional to measure it is the functional giving the smallest contradiction by applying all possible conjunctive rules. We give also the axiomatics of this contradiction measure.
In book
Vol. 9861: Belief Functions: Theory and Applications. , Springer, 2016.
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
N. L. Polyakov, Shamolin M. V., Journal of Mathematical Sciences 2025 Vol. 292 No. 6 P. 793–803
The paper proves a number of properties of a class of non-local aggregation rules that simulate
dynamic aggregation. The work is based on the clan approach in the theory of collective choice, which was
proposed by S. Shelah and developed by the authors. ...
Added: October 8, 2025
N. L. Polyakov, Shamolin M. V., Journal of Mathematical Sciences 2023 Vol. 272 No. 5 P. 667–671
In the paper, combinatorial theorems related to the theory of social choice are obtained. These theorems describe general conditions under which the problem on the preserving the preference set D by anarbitrary aggregation rule f and the problem on the compatibility of the preference set D with a pair (f,C) can be reduced to similar ...
Added: May 19, 2023
Karabekyan D., Журнал Новой экономической ассоциации 2022 № 5(57) С. 24–37
Some distortions are possible in the process of preference aggregation. For example, one voter who is pivotal for some preference profi le may not read instructions properly and accidently submit wrong preference. We study how different voting rules react to these distortions for three, four and fi ve alternatives with computer modelling. One of the ...
Added: January 17, 2023
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
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
Lepskiy A., Meshcheryakova N., , in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2020* 2. Vol. 1238.: Cham: Springer, 2020. P. 283–296.
We apply Dempster-Shafer theory in order to reveal important elements in undirected weighted networks. We estimate cooperation of each node with different groups of vertices that surround it via construction of belief functions. The obtained intensities of cooperation are further redistributed over all elements of a particular group of nodes that results in pignistic probabilities ...
Added: July 8, 2020
Lepskiy A., Smolev V., , in: Atlantis Studies in Uncertainty Modelling, Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)Vol. 1.: Atlantis Press, 2019. P. 321–327.
Added: September 29, 2019
Bronevich A., Rozenberg I., International Journal of Approximate Reasoning 2019 Vol. 112 P. 119–139
In the paper, we formalize the notion of contradiction between belief functions: we argue that belief functions are not contradictory if they provide non-contradictory models for decision-making. To elaborate on this idea, we take the decision rule from imprecise probabilities and show that sources of information described by belief functions are not contradictory iff the ...
Added: September 25, 2019
Springer Nature Switzerland AG, 2019.
Added: September 25, 2019
Bronevich A., Lepskiy A., , in: Proceedings of the 11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)Vol. 1.: P.: Atlantis Press, 2019. P. 328–333.
In real applications, sometimes it is necessary to evaluate inner or external conflict of pieces of evidence. However, these numerical values cannot give us explanations why this conflict occurs. Thus, we need deeper analysis of available information. In the paper, we propose the clusterization of a given evidence on pieces of evidence in a way ...
Added: September 25, 2019
Bronevich A., Rozenberg I., , in: Belief Functions: Theory and Applications 5th International Conference, BELIEF 2018, Compiègne, France, September 17-21, 2018, ProceedingsVol. 11069.: Springer, 2018. P. 31–38.
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 ...
Added: October 8, 2018
Bronevich A., Rozenberg I., International Journal of General Systems 2018 Vol. 27 No. 1 P. 67–96
To model conflict, non-specificity and contradiction in information,
upper and lower generalized credal sets are introduced. Any upper
generalized credal set is a convex subset of plausibility measures
interpreted as lower probabilities whose bodies of evidence consist of
singletons and a certain event. Analogously, contradiction is modelled
in the theory of evidence by a belief function that is greater than
zero ...
Added: February 2, 2018
Andrey G. Bronevich, Rozenberg I., , in: Advances in Intelligent Systems and ComputingVol. 456: Soft Methods for Data Science.: Springer, 2017. P. 87–94.
In the paper we continue investigations started in the paper presented at ISIPTA’15, where the notions of lower and upper generalized credal sets has been introduced. Generalized credal sets are models of imprecise probabilities, where it is possible to describe contradiction in information, when the avoiding sure loss condition is not satisfied. The paper contains ...
Added: October 17, 2016
Springer, 2016.
The theory of belief functions, also referred to as evidence theory or Dempster-Shafer theory, is a well-established general framework for reasoning with uncertainty. It has well-understood connections to other frameworks, such as probability, possibility, and imprecise probability theories. First introduced by Arthur P. Dempster in the context of statistical inference, the theory was later developed ...
Added: September 28, 2016
Lepskiy A., , in: Advances in Intelligent Systems and ComputingVol. 456: Soft Methods for Data Science.: Springer, 2017. P. 311–318.
The qualitative characteristics of the combining evidence with the help of Dempster’s rule with discounting is studied in this paper in the framework of Dempster-Shafer theory. The discount coefficient (discounting rate) characterizes the reliability of information source. The conflict between evidence and change of ignorance after applying combining rule are considered in this paper as ...
Added: September 28, 2016
Bronevich A., Rozenberg I., , in: Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications.: Rome: Aracne editrice, 2015. P. 67–76.
In the paper we consider the generalization of the conjunctive rule in the theory of imprecise probabilities. Let us remind that the conjunction rule, produced on credal sets,gives their intersection and it is not defined if this intersection is empty. In the last case the sources of information are called contradictory1. Meanwhile, in the Dempster-Shafer ...
Added: February 29, 2016