Efficient exact computation of the conjunctive and disjunctive decompositions of D-S Theory for information fusion: Translation and extension
This work addresses a computational bottleneck in evidence-based fusion methods, offering incremental improvements for researchers and practitioners in information fusion domains.
The paper tackles the high computational burden of conjunctive and disjunctive decompositions in Dempster-Shafer Theory for information fusion, proposing a method based on focal points that reduces complexity to linear in some cases and enables tractability for frames of discernment with over a few dozen states.
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.