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### Dempster-Shafer Calculus

The basic idea in representing uncertainty in this model is:

• Set up a confidence interval -- an interval of probabilities within which the true probability lies with a certain confidence -- based on the Belief B and plausibility PL provided by some evidence E for a proposition P.
• The belief brings together all the evidence that would lead us to believe in P with some certainty.
• The plausibility brings together the evidence that is compatible with P and is not inconsistent with it.

• This method allows for further additions to the set of knowledge and does not assume disjoint outcomes.

If is the set of possible outcomes, then a mass probability, M, is defined for each member of the set and takes values in the range [0,1].

The Null set, , is also a member of .

NOTE: This deals wit set theory terminology that will be dealt with in a tutorial shortly. Also see exercises to get experience of problem solving in this important subject matter.

M is a probability density function defined not just for but for em all subsets.

So if is the set { Flu (F), Cold (C), Pneumonia (P) } then is the set { , {F}, {C}, {P}, {F, C}, {F, P}, {C, P}, {F, C, P} }

• The confidence interval is then defined as [B(E),PL(E)]
where

where i.e. all the evidence that makes us believe in the correctness of P, and

where i.e. all the evidence that contradicts P.

dave@cs.cf.ac.uk