Dempster-Shafer Theory

Abstract

This is a theory of evidence potentially suitable for knowledge-based systems. The system is based on “basic probabilities” which can be visualized as probability masses that are constrained to stay within the subset with which they are associated, but are free to move over every point in the subset. From these basic probabilities we can derive upper and lower probabilities (Dempster) or belief functions and plausibilities (Shafer). The means of combining basic probabilities is using Dempster’s Rule which is valid given independent evidences. A position of complete ignorance about an hypothesis is represented by having an upper probability of one and a lower probability of zero. Complete certainty about the probability of an hypothesis is represented when the upper and lower probabilities are equal. The approach can suffer from high computation times, although this can be reduced when each piece of evidence confirms or denies a single proposition rather than a disjunction. The method has been extended to allow fuzzy subsets as an expression of knowledge.