Robust combination rules for evidence theory
Dempster's rule of combination in evidence theory is a powerful tool for reasoning under uncertainty. Since Zadeh highlighted the counter-intuitive behaviour of Dempster's rule, a plethora of alternative combination rules have been purposed. In this paper, we purpose a general formulation for combination rules in evidence theory as a weighted sum of the conjuctive and disjunctive rules. Moreover, with the aim of automatically accounting for the reliability of sources of information, we propose a class of robust combination rules (RCR) in which the weights are a function of the conflict between two pieces of information. The interpretation given to the weight of the conflict between two BPAs is an indicator of the relative reliability of the sources; if the conflict is low, then both sources are reliable, and if the conflict is high, then at least one source is unreliable. We show some interesting properties satisfied by the RCRs, such as positive belief reinforcement or the neutral impact of vacuous belief, and establish links with other classes of rules. The behaviour of the RCRs over non-exhaustive frames of discernment is also studies, as the RCRs implicitly perform a kind of automatic deconditioning through the simple use of the disjunction operator. We focus our study on two special cases: (1) RCR-S, a rule with symmetric coefficients that is proved to the unique and (2) RCR-L, a rule with asymmetric coefficients based on a logarithmic function. Their behaviours are then compared to some classical combination rules proposed thus far in the literature on a few examples, and on Monte Carlo simulations.
robust combination rules evidence theory reliability adaptive weightings information fusion