A Decision Calculus for Belief Functions in Valuation-Based Systems

TL;DR

This paper introduces a decision calculus for Dempster-Shafer belief functions within valuation-based systems, enabling decision-making under uncertainty and reducing to Bayesian calculus when probabilities are used.

Contribution

It proposes a novel decision calculus for belief functions in VBS, incorporating a weighting factor and demonstrating compatibility with existing fusion algorithms.

Findings

The calculus can solve decision problems represented with belief functions.

It reduces to Bayesian probability calculus when probabilities are used.

The approach integrates belief functions into the VBS framework effectively.

Abstract

Valuation-based system (VBS) provides a general framework for representing knowledge and drawing inferences under uncertainty. Recent studies have shown that the semantics of VBS can represent and solve Bayesian decision problems (Shenoy, 1991a). The purpose of this paper is to propose a decision calculus for Dempster-Shafer (D-S) theory in the framework of VBS. The proposed calculus uses a weighting factor whose role is similar to the probabilistic interpretation of an assumption that disambiguates decision problems represented with belief functions (Strat 1990). It will be shown that with the presented calculus, if the decision problems are represented in the valuation network properly, we can solve the problems by using fusion algorithm (Shenoy 1991a). It will also be shown the presented decision calculus can be reduced to the calculus for Bayesian probability theory when probabilities, instead of belief functions, are given.