Abstract
In this paper it is considered the problem of discounting a credal set of probability distributions by a factor \(\alpha \) representing a degree of unreliability of the information source providing the imprecise probabilistic information. An axiomatic approach is followed by giving a set of properties that this operator should satisfy. It is shown that discounting can be defined taking a divergence measure between probabilities as basis. Several examples are given starting from different divergence measures, as the Kullback-Leibler divergence or the total variance divergence. Finally, a characterization of the associated discounting is given in terms of sets of almost desirable gambles for two of these measures, providing a behavioral interpretation on them. The usual discounting of belief functions based on a convex combination with the ignorance is associated with the use of what it is called the minimum ratio divergence.
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