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## The Qualitative Characteristics of Combining Evidence with Discounting

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 important characteristics of quality of combining. The quantity of ignorance is estimated with the help of linear imprecision index. The set of crisp and fuzzy discounting rates for which the value of ignorance after combining does not increases is described.

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Vol. 456: Soft Methods for Data Science. , Springer, 2017

Bronevich A., Rozenberg I. N., 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

Bronevich A., Rozenberg I. N., , 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., Rozenberg I. N., , 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

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., 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., Нечеткие системы и мягкие вычисления 2014 Т. 9 № 2 С. 93-114

Some general schemes and examples of aggregation of two belief functions into a single belief function are considered in this paper. We find some sufficient conditions of change of ignorance when evidences are combined with the help of various rules. It is shown that combining rules can be regarded as pessimistic or optimistic depending on ...

Added: January 20, 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

Eichberger J. T., 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

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., 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

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

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

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