Scale sensitivity in the multiplicative AHP and SMART

The paper considers 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. It demonstrates that the rank order of the impact scores and final scores is scale-independent. Finally the paper shows 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.