A hypothesis testing-based discussion on the sensitivity of means of fuzzy data with respect to data shape

This paper aims to answer the last question from a statistical perspective. More concretely, the analysis of the influence of the choice of trapezoidal fuzzy numbers to model data is to be based on the conclusions from statistical hypothesis testing about the mean values of the involved fuzzy datasets. For this purpose, the p-values of tests have been compared for trapezoidal assessment vs. other frequently used ones, like some LU assessments. The analysis is first performed by developing simulation-based pairwise comparisons, and it is later illustrated and corroborated to some extent with a real-life example. The analysis indicates that the shape of the fuzzy assessment scarcely affects statistical conclusions.