On Jaffray's Decision Model for Belief Functions

摘要

In this paper, two decision models for Dempster-Shafer belief functions proposed by Jaffray and Giang-Shenoy respectively are compared. Jaffray's model is applicable for general belief function while Giang-Shenoy's model works for the partially consonant class (pcb). Pcb has been shown by Walley as the only class that is consistent with the likelihood principle of statistics. While both models share many nice properties such as tractability, the separation of risk attitude, ambiguity attitude from ambiguity belief, they differ on important aspects. The comparison is made possible by application of both models to pcb. It is shown that due to a Hurwicz-type condition imposed on decision under ignorance, Jaffray's approach violates the consequentialism property (analogous to the law of iterated expectation in probability theory) that is satisfied by Giang-Shenoy approach.