How to select a model if we know probabilities with interval uncertainty?

Purpose - When the probability of each model is known, a natural idea is to select the most probable model. However, in many practical situations, the exact values of these probabilities are not known; only the intervals that contain these values are known. In such situations, a natural idea is to select some probabilities from these intervals and to select a model with the largest selected probabilities. The purpose of this study is to decide how to most adequately select these probabilities. Design/methodology/approach - It is desirable to have a probability-selection method that preserves independence. If, according to the probability intervals, the two events were independent, then the selection of probabilities within the intervals should preserve this independence. Findings - The paper describes all techniques for decision making under interval uncertainty about probabilities that are consistent with independence. It is proved that these techniques form a 1-parametric family, a family that has already been successfully used in such decision problems. Originality/value - This study provides a theoretical explanation of an empirically successful technique for decision-making under interval uncertainty about probabilities. This explanation is based on the natural idea that the method for selecting probabilities from the corresponding intervals should preserve independence.