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In recent years, dealing with uncertainty using interval probabilities is receiving considerable attention by researchers. Most of researches related to interval probabilities, such as combination, marginalization, condition, Bayesian inferences, assume interval probabilities are known. How to elicit interval probabilities from subject is a basic problem for the applications of interval probability theory and till now a computational challenge. In this research, the approaches for estimating interval probabilities are proposed with the pair-wise comparison of the possible outcomes to know which one is more likely to occur. The first method is LP-based one. The second method is QP-based one. Interval expectation, interval entropy are investigated. The decision criteria under interval probabilities are given.

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