Scale sensitivity in the multiplicative AHP and SMART

Abstract We consider first a variant of the analytic hierarchy process (AHP) with a one‐parametric class of geometric scales to quantify human comparative judgement and with a multiplicative structure: logarithmic regression to calculate the impact scores of the alternatives at the first evaluation level and a geometric‐mean aggregation rule to calculate the final scores at the second level. We demonstrate that the rank order of the impact scores and final scores is scale‐independent. Finally we show that the multiplicative AHP is an exponential version of the simple multi‐attribute rating technique (SMART). In fact, the multiplicative AHP is concerned with ratios of intervals on the dimension of desirability, whereas SMART analyses differences in the corresponding orders of magnitude.