Calculating Uncertainty Intervals From Conditional Convex Sets of Probabilities
This work addresses a theoretical issue in uncertainty modeling for researchers in probability and decision theory, but it appears incremental as it builds on prior conditioning methods.
The paper tackles the problem of converting possibility distributions derived from conditioning convex sets of probabilities into probability or uncertainty intervals, using Sugeno and Choquet integrals, and compares their behavior through selected examples.
In Moral, Campos (1991) and Cano, Moral, Verdegay-Lopez (1991) a new method of conditioning convex sets of probabilities has been proposed. The result of it is a convex set of non-necessarily normalized probability distributions. The normalizing factor of each probability distribution is interpreted as the possibility assigned to it by the conditioning information. From this, it is deduced that the natural value for the conditional probability of an event is a possibility distribution. The aim of this paper is to study methods of transforming this possibility distribution into a probability (or uncertainty) interval. These methods will be based on the use of Sugeno and Choquet integrals. Their behaviour will be compared in basis to some selected examples.