Analyzing approximation algorithms in the theory of evidence
Anne-Laure Jousselme, Dominic Grenier, Éloi Bossé · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2002
The major drawback of the Dempster-Shafer's theory of evidence is its computational burden. Indeed, the Dempster's rule of combination involves an exponential number of focal elements, that can be unmanageable in many applications. To avoid this problem, some approximation rules or algorithms have been explored for both reducing the number of focal elements and keeping a maximum of information in the next belief function to be combined. Some studies have yet to be done which compare approximation algorithms. The criteria used always involve pignistic transformations, and by that a loss of information in both the original belief function and the approximated one. In this paper, we propose to analyze some approximation methods by computing the distance between the original belief function and the approximated one. This real distance allows then to quantify the quality of the approximation. We also compare this criterion to other error criteria, often based on pignistic transformations. We show results of Monte-Carlo simulations, and also of an application of target identification.