Estimating the attribute weights through evidential reasoning and mathematical programming

An approach for estimating attribute weight is proposed, which is addressed to the problem inverse to the aggregation assessment based on a hierarchy of attributes. Evidential reasoning framework is employed since the assessment on some basic attributes may be uncertain and incomplete. As a by-product, a simple formula for evidence combination for our special case is obtained. The weights are estimated based on the preference given by the decision-maker, and represented as intervals. The more abundant preference the decision-maker shows, the clearer the relation among the basic attributes.