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About Some Clustering Algorithms in Evidence Theory
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 of focal elements, etc. The article discusses some existing algorithms for clustering evidence bodies and suggests some new algorithms and approaches in such clustering.
Publication based on the results of:
Bronevich A., Lepskiy A., International Journal of Approximate Reasoning 2026 Vol. 190 Article 109597
In the paper, we consider three possible types of external conflict in Dempster-Shafer theory and propose its measurement based on functionals evaluating intersection, inclusion and distance between random sets. All proposed functionals can be viewed as extensions of known functionals like Jaccard metric, Jaccard index, and Dice coefficient from usual sets to random sets based ...
Added: February 25, 2026
Lepskiy A., , in: Belief Functions: Theory and Applications: 6th International Conference, BELIEF 2021, Shanghai, China, October 15–19, 2021, ProceedingsVol. 12915.: Springer, 2021. P. 197–206.
Added: October 20, 2021
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
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
A.S. Kharchevnikova, Savchenko A., Optical Memory and Neural Networks (Information Optics) 2018 Vol. 27 No. 4 P. 246–259
The paper considers the use of convolutional neural networks for the concurrent recognition of the gender and age of a person by video records of his face. The emphasis is on the incorporation of the approach into mobile video-recording software. We have investigated the fusion of decisions obtained during the processing of each video frame, ...
Added: November 5, 2018
Lepskiy A., , in: Belief Functions: Theory and Applications 5th International Conference, BELIEF 2018, Compiègne, France, September 17-21, 2018, ProceedingsVol. 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
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
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, 2016Vol. 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
Bronevich A., Lepskiy A., Penikas H. I., , in: Procedia Computer Science. 3rd International Conference on Information Technology and Quantitative Management, ITQM 2015Vol. 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
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., 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
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
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