In belief functions related fields, the distance measure is an important concept, which represents the degree of dissimilarity between bodies of evidence. Various distance measures of evidence have been proposed and widely used in diverse belief function related applications, especially in performance evaluation. Existing definitions of strict and nonstrict distance measures of evidence have their own pros and cons. In this paper, we propose two new strict distance measures of evidence (Euclidean and Chebyshev forms) between two basic belief assignments based on the Wasserstein distance between belief intervals of focal elements. Illustrative examples, simulations, applications, and related analyses are provided to show the rationality and efficiency of our proposed measures for distance of evidence.

This book constitutes the thoroughly refereed proceedings of the 4th International Conference on Belief Functions, BELIEF 2016, held in Prague, Czech Republic, in September 2016. The 25 revised full papers presented in this book were carefully selected and reviewed from 33 submissions. The papers describe recent developments of theoretical issues and applications in various areas such as combination rules; conflict management; generalized information theory; image processing; material sciences; navigation.

This book constitutes the thoroughly refereed proceedings of the Third International Conference on Belief Functions, BELIEF 2014, held in Oxford, UK, in September 2014. The 47 revised full papers presented in this book were carefully selected and reviewed from 56 submissions. The papers are organized in topical sections on belief combination; machine learning; applications; theory; networks; information fusion; data association; and geometry.

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.

This book constitutes the refereed proceedings of the 6th International Conference on Belief Functions, BELIEF 2021, held in Shanghai, China, in October 2021. The 30 full papers presented in this book were carefully selected and reviewed from 37 submissions. The papers cover a wide range on theoretical aspects on mathematical foundations, statistical inference as well as on applications in various areas including classification, clustering, data fusion, image processing, and much more.

The theory of belief functions, also known as evidence theory or Dempster-Shafer theory, was first introduced by Arthur P. Dempster in the context of statistical inference, and was later developed by Glenn Shafer as a general framework for modeling epistemic uncertainty. These early contributions have been the starting points of many important developments, including the Transferable Belief Model and the Theory of Hints. The theory of belief functions is now well established as a general framework for reasoning with uncertainty, and has well understood connections to other frameworks such as probability, possibility and imprecise probability theories. This volume contains the proceedings of the 2nd International Conference on Belief Functions that was held in Compiègne, France on 9-11 May 2012. It gathers 51 contributions describing recent developments both on theoretical issues (including approximation methods, combination rules, continuous belief functions, graphical models and independence concepts) and applications in various areas including classification, image processing, statistics and intelligent vehicles.

In Dempster–Shafer evidence theory, the basic probability assignment (BPA) can effectively represent and process uncertain information. How to transform the BPA of uncertain information into a decision probability remains a problem to be solved. In the light of this issue, we develop a novel decision probability transformation method to realize the transition from the belief decision to the probability decision in the framework of Dempster–Shafer evidence theory. The newly proposed method considers the transformation of BPA with multi-subset focal elements from the perspective of the belief interval, and applies the continuous interval argument ordered weighted average operator to quantify the data information contained in the belief interval for each singleton. Afterward, we present an approach to calculate the support degree of the singleton based on quantitative data information. According to the support degree of the singleton, the BPA of multi-subset focal elements is allocated reasonably. Furthermore, we introduce the concepts of probabilistic information content in this paper, which is utilized to evaluate the performance of the decision probability transformation method. Eventually, a few numerical examples and a practical application are given to demonstrate the rationality and accuracy of our proposed method.