How different are ranking methods for fuzzy numbers? A numerical study

Ranking fuzzy numbers is often a necessary step in many mathematical models, and a large number of ranking methods have been proposed to perform this task. However, few comparative studies exist and nowadays it is still unknown how similar ranking methods are in practice, i.e., how likely they are to induce the same ranking. In this study, by means of numerical simulations, we try to answer this question. We shall discover that there are some very similar methods as well as some outliers. We end the paper interpreting the results and giving some recommendations on the use of ranking methods.