Pignistic Probability Transforms for Mixes of Low- and High-Probability
  Events
  In some real world information fusion situations, time critical decisions
must be made with an incomplete information set. Belief function theories
(e.g., Dempster-Shafer theory of evidence, Transferable Belief Model) have been
shown to provide a reasonable methodology for processing or fusing the
quantitative clues or information measurements that form the incomplete
information set. For decision making, the pignistic (from the Latin pignus, a
bet) probability transform has been shown to be a good method of using Beliefs
or basic belief assignments (BBAs) to make decisions. For many systems, one
need only address the most-probable elements in the set. For some critical
systems, one must evaluate the risk of wrong decisions and establish safe
probability thresholds for decision making. This adds a greater complexity to
decision making, since one must address all elements in the set that are above
the risk decision threshold. The problem is greatly simplified if most of the
probabilities fall below this threshold. Finding a probability transform that
properly represents mixes of low- and high-probability events is essential.
This article introduces four new pignistic probability transforms with an
implementation that uses the latest values of Beliefs, Plausibilities, or BBAs
to improve the pignistic probability estimates. Some of them assign smaller
values of probabilities for smaller values of Beliefs or BBAs than the Smets
pignistic transform. They also assign higher probability values for larger
values of Beliefs or BBAs than the Smets pignistic transform. These probability
transforms will assign a value of probability that converges faster to the
values below the risk threshold. A probability information content (PIC)
variable is also introduced that assigns an information content value to any
set of probability. Four operators are defined to help simplify the
derivations.
