Preference simulation and preference programming: robustness issues in priority derivation

Decision makers often resist having to make what appears to them as precise numerical judgements in fuzzy situations. Pairwise verbal comparisons used in the AHP are fuzzy in the sense that decision maker(s) need not relate verbal judgment to precise numbers; because of the redundancy inherent in each set of judgments, accurate priorities can be derived from such fuzzy verbal judgments. Another way of making fuzzy judgments is to express each judgment as a numerical interval. This paper explores two new approaches for priority derivation when preferences are expressed as interval judgments, one based on a simulation approach and the other based on mathematical programming. The first approach assumes that the interval judgments are uniformly distributed and proceeds to derive the priority vectors and their underlying rank order by randomly sampling from these distribution. This approach provides, in addition to the priority vectors, a measure of robustness given by the probability of rank reversal. The second approach generates a region (if one exists) that encloses all priority vectors derived from inequalities representing the original interval judgments. The two approaches are described and illustrated through a numerical example.