This paper investigates a multiple attribute decision making problem, whose attribute values are interval rough
numbers and has the priority order of attributes. First, the normalized formulas for rough attribute values are given. Then,
based on the definition of the deviation degree for interval rough numbers, an optimization model with maximum of the
deviation of the attribute values is established, and the attribute weights are derived by solving this model. Furthermore,
based on the rough arithmetic and the expected value operator, the expected utility values of the alternatives are calculated
for ranking all alternatives. Finally, a numerical example shows the effectiveness of the proposed method.