Does fuzzification of pairwise comparisons in analytic hierarchy process add any value?

The analytic hierarchy process (AHP) is a widely used multi-criteria decision-making method to address a variety of problems in the presence of conflicting or uncertain criteria. One of the key issue associated with AHP lies in the conversion of human intuition into the numerical values. To address this problem, the integration of fuzzy set theory into classical AHP has emerged as a popular approach. Fuzzy AHP (FAHP) methods represent human preferences using fuzzy numbers to incorporate vague or imprecise information, which allows FAHP methods to capture the inherent fuzziness of human decision-making. FAHP have gained attention from both researchers and practitioners, however, the effectiveness of FAHP methods is still debated. This study conducted a thorough numerical and empirical study to evaluate the efficacy of representing preferences and judgments in the form of fuzzy numbers in the AHP framework. The findings of this study showed that, in general, classical AHP methods yield significantly better (P≤0.05)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(P \le 0.05)$$\end{document} results compared to existing FAHP methods. However, the study also found that there may be some potential benefits to using the FAHP approach, which warrant further investigation.