Interval priorities in the analytic hierarchy process by interval regression analysis

This paper proposes an interval approach for obtaining interval weights of priorities in the analytic hierarchy process reflecting inconsistency of pairwise comparison ratios given by a decision maker. Even if pairwise comparison values with respect to preference are given as crisp values, the priority weights should be estimated as intervals because of a decision maker's uncertainty of judgments. We deal with two types of comparison matrices represented as crisp and interval elements. This allows some uncertainty of estimations made by a decision maker. The proposed approach can obtain the estimated interval priorities. Since interval regression analysis is based on the concept of possibility, the interval weights obtained by the proposed method can be interpreted as the possible ranges estimated from the given data. The sum of widths of the obtained intervals can be regarded as the degree of inconsistency included in the given data. It is emphasized that interval data of preference can obtain the lower and upper models for the estimated weight intervals.