Structuring Bodies of Evidence

TL;DR

This paper introduces two novel structures for organizing bodies of evidence, significantly reducing computational complexity in evidence theory operations without generating all subsets.

Contribution

It proposes a partition-based structure and hierarchical trees to simplify belief function calculations and Dempster's rule, improving efficiency in evidence theory.

Findings

Partitioning by cardinality reduces calculation complexity.

Hierarchical trees further optimize belief and combination computations.

Both methods avoid exhaustive subset generation.

Abstract

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.