The Dempster-Shafer Theory

The initial work introducing Dempster-Shafer (D-S) theory is found in Dempster (1967) and Shafer (1976). Since its introduction the very name causes confusion, a more general term often used is belief functions (both used intermittently here). Nguyen (1978) points out, soon after its introduction, that the rudiments of D-S theory can be considered through distributions of random sets. More furtive comparison has been with the traditional Bayesian theory, where D-S theory has been considered a generalisation of it (Schubert, 1994). Cobb and Shenoy (2003) direct its attention to the comparison of D-S theory and the Bayesian formulisation. Their conclusions are that they have the same expressive power, but that one technique cannot simply take the role of the other. The association with artificial intelligence (AI) is clearly outlined in Smets (1990), who at the time, acknowledged the AI community has started to show interest for what they call the Dempster-Shafer model. It is of interest that even then, they highlight that there is confusion on what type of version of D-S theory is considered. D-S theory was employed in an event driven integration reasoning scheme in Xia et al. (1997), associated with automated route planning, which they view as a very important branch in applications of AI. Liu (1999) investigated Gaussian belief functions and specifically considered their proposed computation scheme and its potential usage in AI and statistics. Huang and Lees (2005) apply a D-S theory model in natural-resource classification, comparing with it with two other AI models. Wadsworth and Hall (2007) considered D-S theory in a combination with other techniques to investigate site-specific critical loads for conservation agencies. Pertinently, they outline its positioning with respect to AI (p. 400);