A Basic Algorithm for Generating Individualized Numerical Scale (BAGINS)

TL;DR

This paper introduces a simple, computationally efficient method for customizing numerical scales for linguistic labels in decision-making, improving consistency over fixed scales in AHP.

Contribution

A novel, easy-to-implement scale individualization method based on compatibility, with new metrics and experimental validation for AHP.

Findings

Scale individualization outperforms fixed scale approaches.

The proposed heuristic is easy to learn and computationally efficient.

Experimental results validate the benefits of the new method.

Abstract

Linguistic labels are 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 to 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 are proposed in the literature. There is a growing interest in scale individualization rather than relying on a generic fixed scale since 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 the transitivity errors, i.e., consistency. In this research, we proposed 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 in particular, numerical and two empirical studies are conducted. The results of the analyses demonstrate that the scale individualization outperforms the conventional fixed scale approach and validates the benefit of the proposed novel heuristic.