A generalization of the Wilcoxon signed-rank test and its applications |
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Authors: | S M Taheri G Hesamian |
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Institution: | 1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran 2. Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, 91779-48974, Iran
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Abstract: | This paper extends the Wilcoxon signed-rank test to the case where the available observations are imprecise quantities, rather than crisp. To do this, the associated test statistic is extended, using the α-cuts approach. In addition, the concept of critical value is generalized to the case when the significance level is given by a fuzzy number. Finally, to accept or reject the null hypothesis of interest, a preference degree between two fuzzy sets is employed for comparing the observed fuzzy test statistic and fuzzy critical value. |
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