Wilcoxon Signed-Rank Test based on Fuzzy Random Variables and Fuzzy Hypotheses

In this paper, the Wilcoxon ranked-sum test is generalized to the fuzzy environment based on a sample of fuzzy random variables. In the proposed approach, first by remembering the concept of induced fuzzy random variable from a family of distributions with fuzzy parameter, the fuzzy median of the population and the fuzzy median of a sample of fuzzy random variables are generalized to the fuzzy environment. The large sample property of a sequence of fuzzy sample mean is then investigated based on a popular fuzzy distance. Then a new method for testing fuzzy hypotheses for fuzzy median of a population is extended based on a criterion of belonging of a fuzzy set to the conventional critical region. For this purpose, the fuzzy Wilcoxon test statistic is first defined based on the fuzzy observations. Finally, at a given level of exact significance, a fuzzy test is proposed to test the fuzzy hypotheses of fuzzy median. The proposed method is finally illustrated with a practical example. The proposed approach is compared with other existing methods and the differences are examined.