Document Type : Research Paper


Department of Statistics, Faculty of Mathematical Sciences and Statistics, University of Birjand, Birjand, Iran


This paper deals with the problem of testing statistical
hypotheses when the available data are fuzzy. In this approach, we
first obtain a fuzzy test statistic based on fuzzy data, and then,
based on a new signed distance between fuzzy numbers, we introduce
a new decision rule to accept/reject the hypothesis of interest.
The proposed approach is investigated for two cases: the case
without nuisance parameters and the case with nuisance parameters.
This method is employed to test the hypotheses for the mean of a
normal distribution with known/unknown variance, the variance of a
normal distribution, the difference of means of two normal
distributions with known/unknown variances, and the ratio of
variances of two normal distributions.


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