Method of imprecision compared to utility theory for design selection problems

Two methods have been proposed for manipulating uncertainty reflecting designer choice: utility theory and the method of imprecision. Both methods represent this uncertainty across decision making attributes with zero to one ranks, higher preference modeled with a higher rank. The two methods can differ, however, in the combination metrics used to combine the ranks of the incommensurate design attributes. Utility theory resolves the multi-attributes using various well proven additive metrics. In contrast, the method of imprecision resolves by also considering non-additive metrics, such as ranking by the worst case performance or by multiplicative metrics. The axioms of utility theory are appropriate for designs where it is deemed the attributes can always be traded off, even to the point of achieving zero preference in some attributes. In the case of a design with attributes which cannot have zero preference, such as stress limits or maximum allowed cost, the method of imprecision is more appropriate: it trades off attribute levels without permitting any of them to be traded off to zero performance.