Fuzzy confidence intervals for mean of Gaussian fuzzy random variables

摘要

A new approach to construct the two-sided and one-sided fuzzy confidence intervals for the fuzzy parameter is introduced, based on normal fuzzy random variables. Fuzzy data, that are observations of normal fuzzy random variables, are used in constructing such fuzzy confidence intervals. We invoke usual methods of finding confidence intervals for parameters obtained form h-level sets of fuzzy parameter to construct fuzzy confidence intervals. The crisp data that are used in constructing these confidence intervals come form h-level sets of fuzzy observations. Combining such confidence intervals yields a fuzzy set of the class of all fuzzy parameters, which is called the fuzzy confidence interval.Then, a criterion is proposed to determine the degree of membership of every fuzzy parameter in the introduced fuzzy confidence interval. A numerical example is provided to clarify the proposed method. Finally, the advantages of the proposed method with respect to some common methods are discussed.