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.
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.
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.