In functional issues, due to lack of precise information and hypotheses and enough assumptions about distribution or the population parameters, the fuzzy nonparametric tests are used. Regarding the fact that the nonparametric tests are based upon ranking observations, it is important to rank the fuzzy observations in order to do nonparametric tests. In this article, a method of ranking fuzzy data is offered based on the Dp,q—distance between two fuzzy numbers and the results of this method are evaluated and compared with other methods. When the data and hypotheses are not precise, the presented method is used to do nonparametric tests related to the median in one or two populations. Finally, some applied examples in management, psychology, and lifetime testing are provided to illustrate the efficiency of proposed approaches. Moreover, the proposed methods are examined to compare with some other existing methods and their effectiveness will be cleared via some numerical examples and some comparison studies.

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