The intersection probability: betting with probability intervals
This work addresses a theoretical gap for researchers in uncertainty reasoning, but it is incremental as it adapts an existing method from belief functions to probability intervals.
The paper tackles the problem of decision making with probability intervals by proposing the intersection probability as a natural transformation, enabling utility-based frameworks analogous to those for belief functions.
Probability intervals are an attractive tool for reasoning under uncertainty. Unlike belief functions, though, they lack a natural probability transformation to be used for decision making in a utility theory framework. In this paper we propose the use of the intersection probability, a transform derived originally for belief functions in the framework of the geometric approach to uncertainty, as the most natural such transformation. We recall its rationale and definition, compare it with other candidate representives of systems of probability intervals, discuss its credal rationale as focus of a pair of simplices in the probability simplex, and outline a possible decision making framework for probability intervals, analogous to the Transferable Belief Model for belief functions.