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AbstractWe 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.

AbstractOne of the most critical issues in many applications of fuzzy sets is the successful evaluation of membership values. A method based on pairwise comparisons provides an interesting way of evaluating membership values. That method was proposed by Saaty, almost 20 years ago, and since then has captured the interest of many researchers around the world. However, recent investigations reveal that the original scale may cause severe inconsistencies in many decision‐making problems. Furthermore, exponential scales seem to be more natural for humans to use in many decision‐making problems. In this paper two evaluative criteria are used to examine a total of 78 scales which can be derived from two widely used scales. The findings in this paper reveal that there is no single scale that can outperform all the other scales. Furthermore, the same findings indicate that a few scales are very efficient under certain conditions. Therefore, for a successful application of a pairwise‐comparison‐based method the appropriate scale needs to be selected and applied.