Decision-making with Belief Functions and pignistic probabilities

Philippe Smets' method of decisionmaking is described, which transforms a Belief Function into a single probability function, the pignistic probabilityfunction, which is equivalent to the standard approach.

Abstract

The paper discusses the different approaches to decision-making using Belief Functions. In particular, I describe Philippe Smets' method of decisionmaking, which transforms a Belief Function into a single probability function, the pignistic probability function. This transformation is sensitive to the choice of frame of discernment, which is often, to a large extent, arbitrary. It thus seems natural to consider all refinements of a frame of discernment and their associated pignistic probability functions and decisions. The main result of the paper is that this is equivalent to the standard approach.