A parametric method has been developed to estimate the fuzzy mean and variance of fuzzy random va... more A parametric method has been developed to estimate the fuzzy mean and variance of fuzzy random variable using Gumbel distribution. It is an extreme value type-I distribution which is a limiting model for the maximum and minimum values of a data set. In order to obtain the fuzzy mean and variance, first, using the method of alpha cut, crisp intervals from each of the fuzzy observation for the same α level are generated. Thereafter, from these crisp intervals for the same α level, the probability distributions of the extreme values and its parameters have been estimated. The interval containing these two parameters as extreme points will represent the estimated crisp interval parameter of the crisp intervals for a certain α level. After estimating all the interval parameters for different levels of alpha cuts, the fuzzy mean and variance of a fuzzy random variable are estimated.
A parametric method has been developed to estimate the fuzzy mean and variance of fuzzy random va... more A parametric method has been developed to estimate the fuzzy mean and variance of fuzzy random variable using Gumbel distribution. It is an extreme value type-I distribution which is a limiting model for the maximum and minimum values of a data set. In order to obtain the fuzzy mean and variance, first, using the method of alpha cut, crisp intervals from each of the fuzzy observation for the same α level are generated. Thereafter, from these crisp intervals for the same α level, the probability distributions of the extreme values and its parameters have been estimated. The interval containing these two parameters as extreme points will represent the estimated crisp interval parameter of the crisp intervals for a certain α level. After estimating all the interval parameters for different levels of alpha cuts, the fuzzy mean and variance of a fuzzy random variable are estimated.
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