Analysis of information inconsistency in belief function theory. Part I: external conflict

The analysis results of information inconsistency within belief function theory (the Dempster–Shafer theory of evidence) are reviewed. This theory has been intensively developing over the past 10–15 years. Part I of the survey considers the measure of external conflict between bodies of evidence. The concepts of conflict and non-conflict bodies of evidence and the basic requirements applied to measures of external conflict are discussed. Different axioms of the measure of external conflict are analyzed. The general forms of measures of external conflict that satisfy the system of axioms are given. Different methods for constructing measures of external conflict (metric, algebraic, and structural approaches; evaluation by combining rules) are presented. The robust estimation of external conflict, the relationship between its measure and the metric on the set of bodies of evidence, and the consistency of combining rules and measures of external conflict are discussed. Many illustrative examples are provided.