Descriptive Comparison of the Rating Scales Through Different Scale Estimates: Simulation-Based Analysis

In dealing with intrinsically imprecise-valued magnitudes, a common rating scale type is the natural language-based Likert. Along the last decades, fuzzy scales (more concretely, fuzzy linguistic scales/variables and fuzzy ratig scales) have also been considered for rating values of these magnitudes. A comparative descriptive analysis focussed on the variability/dispersion associated with the magnitude depending on the considered rating scale is performed in this study. Fuzzy rating responses are simulated and associated with Likert responses by means of a ‘Likertization’ criterion. Then, each ‘Likertized’ datum is encoded by means of a fuzzy linguistic scale. In this way, with the responses available in the three scales, the value of the different dispersion estimators is calculated and compared among the scales.