Abstract
In this article, we first define a normal fuzzy random variable and then, using the α-pessimistic values of the imprecise observations, some methods for testing normality based on fuzzy observations are proposed. Using the popular test statistics, namely Kolmogorov-Smirnov, Cramer von Mises, Kuiper, Anderson-Darling, and Shapiro-Wilk, tests for normality of fuzzy data are constructed. By Monte Carlo simulations, the power values of the proposed tests are computed and then compared to each other under various alternatives. We then formulate some recommendations for the application of the studied tests in practice. Finally, we present an illustrative example which shows how the proposed procedures can be applied to test the goodness-of-fit of normality when a fuzzy sample is available.
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