"On the Evaluation and Application of Different Scales For Quantifying Pairwise
Comparisons in Fuzzy Sets"
Journal of Multi-Criteria Decision Analysis,
1994, Vol. 3, No. 3, pp. 133-155.
E. Triantaphyllou, F.A. Lootsma, P.M. Pardalos, and S.H. Mann
One 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 for evaluating
membership values. That method was proposed by Saaty, almost 20
years ago, and since then it 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.