In a recent paper we have introduced the fuzzy hyperbolic inequality index, to quantify the inequality associated with a fuzzy random variable in a finite population. In previous papers, we have also proven that the classical hyperbolic inequality index associated with real-valued random variables in finite populations can be unbiasedly estimated in random samplings. The aim of this paper is to analyze the problem of estimating the population fuzzy hyperbolic index associated with a fuzzy random variable in random samplings from finite populations. This analysis will lead us to conclude that an unbiased (up to additive equivalences) estimator of the population fuzzy hyperbolic inequality index can be constructed on the basis of the sample index and the expected value of the values fuzzy hyperbolic inequality in the sample.