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

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.

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.

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 and belief functions defined on reals. In addition, for such belief functions, we consider the Wasserstein metric and study its connections to disjunctions of belief functions.

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.

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.

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 addition, measure of conflict between the evidence introduced by axiomatically. A general view of a bilinear measure of conflict found. The upper and lower bounds dependence of the index decreasing of ignorance from the value of measures of the conflict after applying Dempster combination rule found.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.