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## The choice of generalized Dempster-Shafer rules for aggregating belief functions based on imprecision indices.

P. 21-28.

Bronevich A., Розенберг И. Н.

In the paper we investigate the criteria of choosing generalized Dempster-Shafer rules for aggregating sources of information presented by belief functions. The approach is based on measuring various types of uncertainty in information and we use for this linear imprecision indices. Some results concerning properties of such rules are also presented.

### In book

Vol. 8764. , Dordrecht, L., Heidelberg, NY : Springer, 2014

Bronevich A., Розенберг И. Н., International Journal of Approximate Reasoning 2015 Vol. 56 P. 122-136

In the paper we investigate the criteria of choosing generalized Dempster–Shafer rules for aggregating sources whose information is represented by belief functions. The approach is based on measuring various types of uncertainty in information and we use for this purpose in particular linear imprecision indices. Some results concerning properties of such rules are also presented. ...

Added: March 5, 2015

Andrey G. Bronevich, Rozenberg I., , in : Lecture Notes in Artificial Intelligence. Vol. 9861: Belief Functions: Theory and Applications.: Springer, 2016. P. 137-145.

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, ...

Added: October 17, 2016

Bronevich A., Rozenberg I., , in : Belief Functions: Theory and Applications 5th International Conference, BELIEF 2018, Compiègne, France, September 17-21, 2018, Proceedings. Vol. 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

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

Lepskiy A., Bronevich A., International Journal of General Systems 2015 Vol. 44 No. 7-8 P. 812-832

The paper is devoted to the investigation of imprecision indices. They are used for evaluating imprecision (or non-specificity) contained in information described by monotone (non-additive) measures. These indices can be considered as generalizations of the generalized Hartley measure. We argue that in some cases, for example in approximation problems, the application of imprecision indices is ...

Added: September 12, 2015

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

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

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

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

Springer Nature Switzerland AG, 2019

Added: September 25, 2019

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

Bronevich A., Lepskiy A., International Journal of General Systems 2015

The paper is devoted to the investigation of imprecision indices introduced in (Bronevich & Lepskiy, 2003). They are used for evaluating imprecision (or nonspecificity) contained in information described by monotone (non-additive) measures. These indices can be considered as generalizations of the generalized Hartley measure. We argue that in some cases, for example, in approximation problems ...

Added: December 12, 2014

Lepskiy A., , in : Advances in Intelligent Systems and Computing. Vol. 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., Penikas H. I., Lepskiy A. et al., / Высшая школа экономики. Серия WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2015. № 10.

There is one of the investment strategies on a stock market called a choice of securities including
its buying and sale based on financial analysts’ recommendations. The distinguishing characteristic of
these recommendations is that in each of it for the same securities there can be different recommendations
(«Buy», «Sell», «Hold») as well as for one type of recommendations ...

Added: December 2, 2015

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