General Schemes of Combining Rules and the Quality Characteristics of Combining

Lepskiy Alexander

Book chapter

General Schemes of Combining Rules and the Quality Characteristics of Combining

P. 29-38.

Lepskiy A.

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 the sign of the change of ignorance after applying.

Language: English

Full text (PDF, 160 Kb)

Text on another site

Keywords: combining rules change of ignorance

Publication based on the results of: Theoretical and numerical study of advanced mathematical models in the social, economic, political and financial fields(2014)

In book

General Schemes of Combining Rules and the Quality Characteristics of Combining

Belief Functions: Theory and Applications

Edited by: F. Cuzzolin. Vol. 8764. Heidelberg; NY; L.; Dordrecht: Springer, 2014.

On the Conflict Measures Agreed with the Combining Rules

Lepskiy A. In bk.: 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 the metric and entropy components can be distinguished in such measures. Moreover, these components are changed differently after combining of the bodies of evidence.

Added: Sep 24, 2018

About Relation between the Measure of Conflict and Decreasing of Ignorance in Theory of Evidence

Lepskiy A. In bk.: Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13). Amsterdam; Beijing; P.: 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 relationships between the measure of conflict and the index of decreasing of ignorance in the case of different types of evidences and the application of different combining rules were investigated.

Added: Sep 22, 2013

Belief Functions: Theory and Applications 5th International Conference, BELIEF 2018, Compiègne, France, September 17-21, 2018, Proceedings

Vol. 11069. 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) as well as on applications in various areas including classification, statistics, data fusion, network analysis and intelligent vehicles.

Added: Sep 24, 2018

Aggregation of Forecasts and Recommendations of Financial Analysts in the Framework of Evidence Theory

Lepskiy A., Кутынина Е. А. In bk.: Advances in Fuzzy Logic and Technology 2017. Vol. 642. Cham: Springer, 2018. P. 370-381.

The article is dedicated to the method of aggregation of financial analysts’ recommendations in the framework of the evidence theory. This method considered on the example of Russian stock market and the quality of the obtained results was compared with the classical consensus forecast. It is shown that the combination rules, which are widely developed in the theory of evidence, allow aggregating the recommendations of analysts taking into account the historical reliability of information sources, the nature of the taken decisions (pessimism-optimism), the conflict between forecasts and recommendations, etc. In most cases it turned out that, obtained aggregated forecasts are more accurate than consensus forecast.

Added: Oct 5, 2017

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. Therefore, an internal conflict can be considered as an external conflict of decomposition of the original body of evidence. This approach is specified in the article for decomposition by the Dempster rule and decomposition by the disjunctive consensus rule. The possible limits of change of the internal conflict are found in the case of these two combining rules for single-focal (categorical) and two-focal bodies of evidence. The decomposition method is discussed in detail for the case of a universal set with two alternatives.

Added: Sep 17, 2020

Application of the Belief Function Theory to the Development of Trading Strategies

Lepskiy A., Suevalov A. Procedia Computer Science. 2019. Vol. 162. P. 235-242.

The possibility of using the belief function theory for developing of trading strategies is considered in this paper. An analysis of this approach is given on the data of the Russian stock market. The belief and plausibility functions (and their corresponding bodies of evidence) to the system’s recommendations (buy, sell or hold) are calculated using fuzzy inference methods for technical indicators. Further, these bodies of evidence are aggregated using the combining rules (Dempster’s rule, Yager’s rule and others). The discount coefficients of the bodies of evidence are calculated at the stage of the learning under the condition of maximizing the profitability of the trading strategy. The intervals for the buying or selling of assets are determined on the results of such combination. The decision about the corresponding action is taken after comparing these intervals. The study showed that the proposed approach provides an interesting result.

Added: Jan 1, 2020