Interval evaluations in the analytic hierarchy process by possibility analysis

Since a pairwise comparison matrix in the Analytic Hierarchy Process (AHP) is based on human intuition, the given matrix will always include inconsist ent elements violating the transitivity property. We propose the Interval A I IP by which interval weights can be obtained. The widths of the estimated interval weights represent inconsistency in judging data. Since interval w eights can be obtained from inconsistent data, the proposed Interval AI-IP is more appropriate to human judgment. Assuming crisp values in a pairwise comparison matrix, the interval comparisons including the given crisp compa risons can be obtained by applying the Linear Programming (LP) approach. Us ing an interval preference relation, the Interval AHP for crisp data can be extended to an approach for interval data allowing to express the uncertai nty of human judgment in pairwise comparisons.