Aiming at the uncertainty and preference reversal in practical decision making problems, an approach for multiattribute decision making under interval uncertainty is proposed. The interval assessments are integrated by the evidential reasoning at first, then the prospect value of each alternative is worked out by cumulative prospect theory, substituting for subjective expected utility theory, to handle with preference reversal in possibility under uncertainty, interval possibility degree is used to order all alternatives at last. In this paper, the process of decision making is provided, a pair of nonlinear programming models is built up to calculate the overall prospect value of each alternatives, and the feasibility, rationality and effectiveness of this approach are illustrated using an example.