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 (*} then is the set { , {*F*), Cold (*C*), Pneumonia (*P*)*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