Monte Carlo and quasi-Monte Carlo methods for Dempster's rule of combination

One of the challenges in Dempster-Shafer theory is that the data fusion calculation resulting from the popular Dempster's rule of combination is #P-complete. This imposes a computational constraint on the number of belief functions and the number of focal sets that can be combined using Dempster's rule. In this paper we develop Monte Carlo algorithms to approximate Dempster's rule of combination. The algorithms incorporate importance sampling and low-discrepancy sequences. Numerical results suggest the algorithms make it possible to apply Dempster's rule to a much larger number of belief functions and focal sets, and consequently widen the scope of applications of Dempster-Shafer theory. (c) 2022 Elsevier Inc. All rights reserved.