Лепский Александр Евгеньевич

Belief Functions for the Importance Assessment in Multiplex Networks

2020 · CHAPTER · en

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 of node-to-node interactions. Finally, pairwise interactions can be aggregated into the centrality vector that ranks nodes with respect to derived values. We also adapt the proposed model to multiplex networks. In this type of networks nodes can be differently connected with each other on several levels of interaction. Various combination rules help to analyze such systems as a single entity, that has many advantages in the study of complex systems. In particular, Dempster rule takes into account the inconsistency in initial data that has an impact on the final centrality ranking. We also provide a numerical example that illustrates the distinctive features of the proposed model. Additionally, we establish analytical relations between a proposed measure and classical centrality measures for particular graph configurations.

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

2020 · ARTICLE · en

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.

Clustering a Body of Evidence Based on Conflict Measures

2019 · CHAPTER · en

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 that we try to achieve the highest conflict among pieces of evidence and the smallest inner conict within pieces of evidences based on several functionals that help us to evaluate inner and external conflict.

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

2019 · CHAPTER · en

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

2019 · ARTICLE · en

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.

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

2018 · CHAPTER · en

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.

Application of Fuzzy Asymmetric GARCH-Models to Forecasting of Volatility of Russian Stock Market

2018 · CHAPTER · en

This paper presents the results of volatility forecasting for indices of the Russian stock market using existing and developed by the authors fuzzy asymmetric GARCH-models. These models consider various switching functions which are taking into account the positive and negative shocks and are built using the tools of fuzzy numbers. Furthermore, in some models there are used switching functions that consider expert macroeconomic information. It was shown that fuzzy asymmetric GARCH-models provide a more accurate prediction of volatility than similar crisp models.

On the Preservation of Comparison of Distorted Histograms

2018 · ARTICLE · en

The necessity of comparison of histograms with the help of relationship of type “more or less” arises in many problems of decision-making. There are many approaches to solve this problem. But the histograms can be distorted. Then, we have to find the conditions on the distortions under which the comparison of the two histograms does not change. The solution of this problem is researched in the paper with respect to three popular probabilistic methods of comparison.

On the Conflict Measures Agreed with the Combining Rules

2018 · CHAPTER · en

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.

Dynamic Analysis of the Development of Scientific Communities in the Field of Soft Computing

2017 · CHAPTER · en

This paper is dedicated to the research of the dynamics of development and interactions among several scientific communities in the field of fuzzy logic and soft computing. This analysis was performed with the help of the following characteristics: conferences participants’ renewal, the level of cooperation in scientific communities, participation of one community’s key players in activities of the other ones, comparative number of most active participants in each community, uniformity of key players’ participation in different conferences.