Efficient exact computation of the conjunctive and disjunctive decompositions of D-S Theory for information fusion: Translation and extension

TL;DR

This paper introduces a novel method leveraging the concept of focal points to efficiently compute the conjunctive and disjunctive decompositions in Dempster-Shafer Theory, significantly reducing computational complexity for large frames of discernment.

Contribution

It presents a new approach that exploits evidence structure to achieve linear complexity in computing key decompositions in DST, extending previous work to larger problem sizes.

Findings

Reduces computation time for evidence decompositions

Achieves linear complexity in the number of focal sets

Potentially scalable to frames with dozens of states

Abstract

Dempster-Shafer Theory (DST) generalizes Bayesian probability theory, offering useful additional information, but suffers from a high computational burden. A lot of work has been done to reduce the complexity of computations used in information fusion with Dempster's rule. Yet, few research had been conducted to reduce the complexity of computations for the conjunctive and disjunctive decompositions of evidence, which are at the core of other important methods of information fusion. In this paper, we propose a method designed to exploit the actual evidence (information) contained in these decompositions in order to compute them. It is based on a new notion that we call focal point, derived from the notion of focal set. With it, we are able to reduce these computations up to a linear complexity in the number of focal sets in some cases. In a broader perspective, our formulas have the potential to be tractable when the size of the frame of discernment exceeds a few dozen possible states, contrary to the existing litterature. This article extends (and translates) our work published at the french conference GRETSI in 2019.