Fuzzy confidence intervals for mean of Gaussian fuzzy random variables

• Published in: Expert systems with applications 2011-05, Vol.38 (5), p.5240-5244
• Main Authors: Chachi, J., Taheri, S.M.
• Format: Article
• Language: English
• Subjects: Confidence intervals; Construction; Crisps; Fuzzy; Fuzzy confidence interval; Fuzzy logic; Fuzzy parameter; Fuzzy random variable; Fuzzy set theory; Gaussian (normal) fuzzy random variable; Mathematical models; Random variables
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2010.10.034

► The classical confidence intervals are not suitable for dealing with imprecise data. ► Indeed, such confidence intervals could not consider the fuzzy parameters. ► Fuzzy confidence interval (FCI) is introduced and investigated for the above situations. ► A procedure is given to obtain the membership of each fuzzy parameter in the FCI. ► The proposed method has some advantages with respect to the common methods. 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.