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## Application of Non-additive Measures and Integrals for Analysis of the Importance of Party Positions for Voting

P. 321-327.

Lepskiy A., Smolev V.

Keywords: conflict measureChoquet integralBelief functionsNon-additive measuresPolitical science analysis

Publication based on the results of:

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

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

Bronevich A., Lepskiy A., Penikas H. I., Procedia Computer Science 2015 Vol. 55 P. 1113-1122

This paper is devoted to modern approaches to the estimation of external conflict in the theory of evidence based on axioms. The conflict measure is defined on the set of beliefs obtained from several sources of information. It is shown that the conflict measure should be a monotone set function with respect to sets of ...

Added: August 16, 2015

Decompositional approach for evaluation of internal conflict in the framework of the evidence theory

Lepskiy A., Нечеткие системы и мягкие вычисления 2020 Vol. 15 No. 1 P. 43-63

The concept of conflict is one of the central in the belief functions theory. There are differences between external and internal conflicts. A new method for estimating the internal conflict is proposed and studied in this paper. This method assumes that the original body of evidence was derived from simpler evidence using some combining rule. ...

Added: September 17, 2020

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

Lepskiy A., , in : Belief Functions: Theory and Applications 5th International Conference, BELIEF 2018, Compiègne, France, September 17-21, 2018, Proceedings. Vol. 11069.: Springer, 2018. P. 172-180.

The conflict measures induced by the conjunctive and disjunctive combining rules are studied in this paper in the framework of evidence theory. The coherence of conflict measures with combining rules is introduced and studied. In addition, the structure of conjunctive and disjunctive conflict measures is studied in the paper. In particular, it is shown that ...

Added: September 24, 2018

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

Springer, 2018

This book constitutes the refereed proceedings of the 5th International Conference on Belief Functions, BELIEF 2018, held in Compiègne, France, in September 2018.The 33 revised regular papers presented in this book were carefully selected and reviewed from 73 submissions. The papers were solicited on theoretical aspects (including for example statistical inference, mathematical foundations, continuous belief functions) ...

Added: September 24, 2018

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

Lepskiy A., Нечеткие системы и мягкие вычисления 2013 Т. 8 № 2 С. 65-82

The index of decreasing of ignorance after applying of combination rules is introduced and studied in the work within the frame of Dempster-Shafer theory. This index is analysed for some special sets (bodies) of evidence. It is shown that a strong correlation between bodies of evidence is a sufficient condition to decrease of ignorance after applying of combination rules. In ...

Added: December 16, 2013

Bronevich A., Lepskiy A., Penikas H. I., , in : Procedia Computer Science. 3rd International Conference on Information Technology and Quantitative Management, ITQM 2015. Vol. Volume 55.: Amsterdam : Elsevier, 2015. P. 1113-1122.

This paper is devoted to modern approaches to the estimation of external conflict in the theory of evidence based on axioms. The conflict measure is defined on the set of beliefs obtained from several sources of information. It is shown that the conflict measure should be a monotone set function with respect to sets of ...

Added: May 12, 2016

Springer Nature Switzerland AG, 2019

Added: September 25, 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

Lepskiy A., , in : Data Analysis and Optimization. In Honor of Boris Mirkin's 80th Birthday. : Springer, 2023. Ch. 12. P. 179-190.

The Dempster-Shafer theory of evidence considers data that have a frequency-set nature (the so-called body of evidence). In recent years, there has been interest in clustering such objects to approximate them with simpler bodies of evidence, to analyze the inconsistency of information, reducing the computational complexity of processing algorithms, revealing the structure of the set ...

Added: September 29, 2023

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., 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

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

Bronevich A., Розенберг И. Н., , in : Belief Functions: Theory and Applications. Vol. 8764.: Dordrecht, L., Heidelberg, NY : Springer, 2014. P. 21-28.

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. ...

Added: March 5, 2015

Lepskiy A., , in : Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13). : P., Beijing, Amsterdam : Atlantis Press, 2013. P. 355-362.

The conflict measure and index of decreasing of igno-rance in frame of Dempster-Shafer theory are intro-duced. Those functionals are analyzed on the bodies of evidences of special type. It is shown that the great correlation between the bodies of evidence is a sufficient condition of decreasing of ignorance after the applying of combining rule. The ...

Added: September 22, 2013

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

Bronevich A., Розенберг И. Н., Fuzzy Optimization and Decision Making 2014 Vol. 13 No. 1 P. 49-71

This paper gives a way of analyzing decisions in the case of unknown utility function, or more precisely, when we know only a linear order on an income space. It is shown that in this situation, decisions and corresponding probability measures are partially ordered, and this order is identical to the inclusion relation of comonotone ...

Added: September 25, 2013

Lepskiy A., , in : Belief Functions: Theory and Applications: 6th International Conference, BELIEF 2021, Shanghai, China, October 15–19, 2021, Proceedings. Vol. 12915.: Springer, 2021. P. 197-206.

Added: October 20, 2021

Bronevich A., Lepskiy A., Penikas H. I., , in : SCAKD 2016 – The Second International Workshop on Soft Computing Applications and Knowledge Discovery. Proceedings of the Second International Workshop on Soft Computing Applications and Knowledge Discovery. July 18, 2016. Vol. 1687.: CEUR Workshop Proceedings, 2016. P. 12-23.

This article is devoted to the analysis of coherence of financial recommendations with respect to securities of the Russian companies. The study is based on the analysis of approximately 4000 recommendations and forecasts of 23 investment banks with respect to around forty securities of Russian stock market over the period of 2012-2014 years. The predictive ...

Added: September 28, 2016