The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the major points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that aim at reducing the number of focal elements in the belief functions involved. This article reviews a number of algorithms based on this method and introduces a new one—the DI algorithm—that was designed to bring about minimal deviations in those values that are relevant to decision making. It describes an empirical study that examines the appropriateness of these approximation procedures in decision-making situations. It presents and interprets the empirical findings along several dimensions and discusses the various tradeoffs that have to be taken into account when actually applying one of these methods.
