TESTING STATISTICAL HYPOTHESES UNDER FUZZY DATA an‎d BASED ON A NEW SIGNED DISTANCE

This paper deals with the problem of testing statistical hypothe- ses when the available data are fuzzy. In this approach, we rst 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 distribu- tion, the dierence of means of two normal distributions with known/unknown variances, and the ratio of variances of two normal distributions.