Bootstrap approach in hypothesis testing of variance for fuzzy random variables

The purpose of this paper is to express and calculate the variance confidence interval with the Chachi method of data conversion and without converting the initial data with the bootstrap method. Because the data conversion depends on the amount of variance in the denominator of the conversion expression, it fluctuates and as a result, estimating the confidence intervals and testing the hypothesis is challenged. The results of both methods are compared and their advantages and disadvantages are examined. For this purpose, they first deal with concepts such as the fuzzy random variable and the distance between fuzzy data based on the concept of α-shak as well as α -cut. The hypothesis testing process is then performed for the variance of a sample fuzzy data. The bootstrap method was used to test the hypothesis and the mentioned confidence intervals were compared with the confidence intervals obtained by α -bresh method.