A computationally efficient approximation of Dempster-Shafer theory

A Bayesian approximation of a belief function is defined and it is shown that combining the Bayesian approximations of belief functions is computationally less involving than combining the belief functions themselves.

Abstract

An often mentioned obstacle for the use of Dempster-Shafer theory for the handling of uncertainty in expert systems is the computational complexity of the theory. One cause of this complexity is the fact that in Dempster-Shafer theory the evidence is represented by a belief function which is induced by a basic probability assignment, i.e. a probability measure on the powerset of possible answers to a question, and not by a probability measure on the set of possible answers to a question, like in a Bayesian approach. In this paper, we define a Bayesian approximation of a belief function and show that combining the Bayesian approximations of belief functions is computationally less involving than combining the belief functions themselves, while in many practical applications replacing the belief functions by their Bayesian approximations will not essentially affect the result.