Fibonacci Series-Based Pairwise Comparison Scale for Analytic Hierarchy Process

Abstract

The Analytic Hierarchy Process (AHP) is one of the most widely used quantitative tools in multi-criteria decision-making problems. Despite its popularity and use due to its simple but systematic procedure, AHP has limitations especially in terms of the numerical comparison scale used in one of its core steps: pairwise comparisons. AHP is based on verbal comparisons of alternatives/criteria, which are, then, converted into quantitative scores with a one-to-one mapping between the verbal comparisons and a predetermined numerical scale. The choice of the numerical scale affects an essential characteristic of pairwise comparisons: consistency. In order to understand the intrinsic consistency propinquities, this study evaluates the most widely used numerical pairwise comparison scale (Fundamental Scale) and other numerical scales that have been proposed since the initial formulation of AHP. After identifying the limitations of known scales, a new scale based on Fibonacci series is developed considering these limitations, and further analysis is conducted through extensive simulations. The results show that the proposed scale performs well when compared to the other scales.