Preference programming through approximate ratio comparisons

In the context of hierarchical weighting, this paper operationalizes interval judgements which allow the decision maker to enter ambiguous preference statements by indicating the relative importance of factors as intervals of values on a ratio scale. Through such judgements the decision maker can capture the subjective uncertainty in his preferences and thus avoid the often cumbersome elicitation of exact ratio estimates. After each new statement the interval judgements are synthesized into dominance relations on the alternatives by solving a series of linear programming problems. This leads to an interactive process of preference programming which provides more detailed results as the decision maker gradually enters a more specific preference description. Moreover, the overall effort of preference elicitation is smaller than in the analytic hierarchy process because the most preferred alternative can usually be identified before all possible comparisons between pairs of factors have been completed.