Impacts of fundamental scale on the final scores in pairwise comparisons

Abstract

Elicitation of the elements of a pairwise comparison matrix (PCM) is a crucial step in the application of certain multi-attribute models. The Analytic Hierarchy Process (AHP -- Saaty, 1980), and other PCM-based methods use Saaty's fundamental scale frequently. The values of the scale from 1 to 9 have verbal interpretation, and the decision maker can choose without knowing the quantitative scores. Properties of the verbal scale have less attention in the literature; the focus of the publications is on finding the best ratio scale for estimating the preference values. The first part of this paper deals with the scale; however, the analysis concentrates on the interpretation of the elements of the verbal scale, conversion to one of the well-known ratio scales is not in our focus. Individual interpretation of the verbal scale differs, as it has been described in Pöyhönen, H\"{a}m\"{a}l\"{a}inen és Salo (1997), and recently in Dong et al. (2013). The differences are important in the case of group decision making, because if the usual aggregation techniques have been applied, they could lead to biased results, as it was described in the paper of Rokou and Kirytopoulos (2014). The second part of this paper analyses various cases of scale interpretation, concluding in some comments based on the works of Arrow (1979) and Kahneman (2013). The paper proposes a systematic empirical approach for investigating the potential impacts. It aims to contribute to a new empirical study in this field.