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

In assessing fuzzy numbers to model imprecise data associated with random experiments, trapezoidal fuzzy numbers are often considered. Such an assessment is mainly due to easing both interpretation and computation. This becomes especially noticeable when those assessing fuzzy numbers to data have a weak knowledge, low background and little or no expertise in using fuzzy sets (as it happens when questionnaires whose responses involve a free fuzzy rating are conducted), since the required training to explain the meaning and use of trapezoidal fuzzy numbers is definitely lower than that associated with other shapes. Nevertheless, a question that constantly arises in connection with this trapezoidal assessment is whether it can importantly affect the conclusions of the study involving such data.