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