5. Concluding remarks
In this paper, we presented an AHP-based decision-making method for uncertain judgments that include a range of interval ratios: loose articulation, minimum number of interval ratios, and general interval ratios. Our approach is distinct from previous studies in several ways. First, we deal with interval ratios in a unified framework in which the extreme points of the loose articulation can be obtained by a formula or dual programming approach, and those for a minimum number of interval ratios and the general interval ratios can be obtained by a simple procedure.