De-combination of belief function based on optimization

In the theory of belief functions, the evidence combination is a kind of decision-level information fusion. Given two or more Basic Belief Assignments (BBAs) originated from different information sources, the combination rule is used to combine them to expect a better decision result. When only a combined BBA is given and original BBAs are discarded, if one wants to analyze the difference between the information sources, evidence de-combination is needed to determine the original BBAs. Evidence de-combination can be considered as the inverse process of the information fusion. This paper focuses on such a defusion of information in the theory of belief functions. It is an under-determined problem if only the combined BBA is available. In this paper, two optimization-based approaches are proposed to de-combine a given BBA according to the criteria of divergence maximization and information maximization, respectively. The new proposed approaches can be used for two or more information sources. Some numerical examples and an example of application are provided to illustrate and validate our approaches.