Scale sensitivity in the multiplicative AHP and SMART

  • Lootsma F
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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.

Author-supplied keywords

  • AHP
  • Direct rating rank preservation
  • Geometric scales
  • Pairwise comparisons

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  • F. A. Lootsma

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