A basic algorithm for generating an individualized numerical scale

Abstract

Linguistic labels are an effective means of expressing qualitative assessments because they account for the uncertain nature of human preferences. However, to perform computations with linguistic labels, they must first be converted into numbers using a scale function. Within the context of the Analytic Hierarchy Process (AHP), the most popular scale used to represent linguistic labels numerically is the linear 1–9 scale, which was proposed by Saaty. However, this scale has been criticized by several researchers, and various alternatives have been proposed. There is a growing interest in scale individualization rather than relying on a generic fixed scale because the perceptions of the decision maker regarding these linguistic labels are highly subjective. The methods proposed in the literature for scale individualization focus on minimizing transitivity errors (i.e., consistency). In this paper, we propose a novel, easy-to-learn, easy-to-implement, and computationally less demanding scale individualization approach based on compatibility. We also developed an experimental setup and introduced two new metrics that can be used by researchers that contribute to the theory of AHP. To assess the value of scale individualization in general and the performance of the proposed novel approach, numerical and two empirical studies were conducted. The results of the analyses demonstrate that scale individualization outperforms the conventional fixed-scale approach and validates the benefits of the proposed novel heuristic.