Combination of Evidence Using the Principle of Minimum Information Gain
  One of the most important aspects in any treatment of uncertain information
is the rule of combination for updating the degrees of uncertainty. The theory
of belief functions uses the Dempster rule to combine two belief functions
defined by independent bodies of evidence. However, with limited dependency
information about the accumulated belief the Dempster rule may lead to
unsatisfactory results. The present study suggests a method to determine the
accumulated belief based on the premise that the information gain from the
combination process should be minimum. This method provides a mechanism that is
equivalent to the Bayes rule when all the conditional probabilities are
available and to the Dempster rule when the normalization constant is equal to
one. The proposed principle of minimum information gain is shown to be
equivalent to the maximum entropy formalism, a special case of the principle of
minimum cross-entropy. The application of this principle results in a monotonic
increase in belief with accumulation of consistent evidence. The suggested
approach may provide a more reasonable criterion for identifying conflicts
among various bodies of evidence.
