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Scale sensitivity in the multiplicative AHP and SMART
Author(s) -
Lootsma F. A.
Publication year - 1993
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/mcda.4020020205
Subject(s) - multiplicative function , analytic hierarchy process , geometric mean , scale (ratio) , logarithmic scale , mathematics , rank (graph theory) , logarithm , statistics , parametric statistics , sensitivity (control systems) , judgement , simple (philosophy) , dimension (graph theory) , computer science , mathematical economics , combinatorics , engineering , mathematical analysis , philosophy , physics , epistemology , quantum mechanics , electronic engineering , political science , acoustics , law
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.