Case Study-Based Sensitivity Analysis of Scale Estimates w.r.t. the Shape of Fuzzy Data

For practical purposes, and to ease both the drawing and the computing processes, the fuzzy rating scale was originally introduced assuming values based on such a scale to be modeled by means of trapezoidal fuzzy numbers. In this paper, to know whether or not such an assumption is too restrictive, we are going to examine on the basis of a real-life example how statistical conclusions concerning location-based scale estimates are affected by the shape chosen to model imprecise data with fuzzy numbers. The discussion will be descriptive for the considered scale estimates, but for the Frechet-type variance it will be also inferential. The study will lead us to conclude that statistical conclusions are scarcely influenced by data shape.