Decision Making under Subjective Uncertainty

The uncertainty may be classified into two major groups, "objective uncertainty" and "subjective uncertainty". The subject of this article is the decision making under subjective uncertainty. One of the formal models that deal with subjective uncertainty, the mathematical theory of evidence, is extended and its counter-intuitive behavior corrected, allowing the making of correct decisions in a wider range of situations than the original model. The mathematical theory of evidence, or Dempster-Shafer theory, is a popular formalism to model someone's degrees of belief. This theory provides a method for combining evidence from different sources without prior knowledge of their distributions, it is also possible to assign probability values to sets of possibilities rather than to single events only, and it is unnecessary to divide all the probability values among the events, once the remaining probability should be assigned to the environment and not to the remaining events, thus modeling more naturally certain classes of problems. However, it has some pitfalls caused by the non-natural embodiment of the uncertainty in the results. In this paper we present a method of automatic embodiment of the uncertainty that overcomes the aforementioned pitfalls, allowing the combination of evidence with higher degrees of conflict, and avoiding the excessive tendency toward the common possibility of otherwise disjoint hypotheses. This is accomplished by means of a new rule of combination of bodies of evidence that embodies in the numeric results the unknown belief and conflict among the evidence, naturally modeling the epistemic reasoning