Structuring Bodies of Evidence
This work addresses computational bottlenecks in evidence theory for researchers and practitioners, but it is incremental as it builds on existing methods to improve efficiency.
The paper tackles the problem of high computational complexity in evidence theory operations by proposing two structures: one partitions focal elements by cardinality to reduce complexity in calculating belief functions, and the other uses hierarchical trees to further reduce complexity for belief functions and Dempster's rule, without needing to generate all subsets.
In this article we present two ways of structuring bodies of evidence, which allow us to reduce the complexity of the operations usually performed in the framework of evidence theory. The first structure just partitions the focal elements in a body of evidence by their cardinality. With this structure we are able to reduce the complexity on the calculation of the belief functions Bel, Pl, and Q. The other structure proposed here, the Hierarchical Trees, permits us to reduce the complexity of the calculation of Bel, Pl, and Q, as well as of the Dempster's rule of combination in relation to the brute-force algorithm. Both these structures do not require the generation of all the subsets of the reference domain.