On the evaluation and application of different scales for quantifying pairwise comparisons in fuzzy sets

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Abstract
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 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.