Selection rules for new focal elements in the Dempster-Shafer evidence theory

We consider the problem of choosing new focal elements to supplement the given evidence within the framework of the Dempster-Shafer evidence theory. We propose and analyze some selection rules to solve this problem under the assumption that the final goal is to add evidence to make the pignistic transformation of the new body of evidence as representative as possible of the underlying distribution of evidence. Given the current absence of selection rules, we used the random choice of the next focal element as a benchmark, and then we formalized some possible selection rules, some of them based on the maximization or minimization of uncertainty. Then, we used a Monte Carlo simulation to compare the proposed selection rules with the benchmark represented by the random selection. Numerical results show that the selection rule that balances the occurrence of elements of the frame of discernment within the set of focal elements outperforms the others, on average, as well as in a worst-case scenario, and consequently may reasonably serve as a guiding rule for the selection of new focal elements.