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In the framework of interval decision making, the available information is vague and numerically imprecise and the decision situation is modelled by imprecise probabilities and utilities that are simply represented by suitable intervals and comparisons. Alternatives are therefore evaluated in terms of interval expected utilities, which are then used for expressing crisp preferences among these alternatives. In this work, we use the overlap of the above interval expected utilities for expressing valued preferences among the alternatives. In particular, a chain of interval order relations associated with the constructed valued preference relation is studied and the concept of admissibility is expressed in terms of non-dominated alternatives induced by such relations.