Statistical inference of fuzzy weighted regression based on bootstrap approach

In this article, the hypothesis test and confidence interval for the fuzzy coefficients in the fuzzy weighted regression model with precise inputs and fuzzy outputs are discussed. By applying the weighted estimation method in estimating the coefficients and using the conventional fuzzy hypotheses in the fuzzy environment,, We are trying to determine the distribution of the available estimators, based on the bootstrap method so that we can decide to accept or reject the existing hypotheses. Therefore, at first, the required test statistics are calculated based on the bootstrap method. Then, by comparing the probability value and the given significance level, as in the classical method, the null hypothesis is accepted or rejected. Also, from another point of view, hypothesis testing based on bootstrap confidence intervals is also discussed. At the end, by analyzing a practical example with real data in housing, the approach investigated in hypothesis testing and confidence interval for the coefficients of the fuzzy regression model has been analyzed.