This paper introduces a parametric approach for computing the fuzzy monetary (FM) index. We establish the relationship between this fuzzy index, which is frequently used to estimate inequality, and the Generalized Gini index through a parameter, α, that reflects the degree of aversion to inequality. While, for the Generalized Gini index α is chosen by the researcher for the FM index it is derived from data. To efficiently estimate FM, we first prove some technical results and then introduce a parametric method that accelerates the computation of α, incorporating the closed-form expression of the Generalized Gini index for selected distributions. To assess the variability of the index, we propose a parametric bootstrap method. The results are validated through simulations, where we compare the original FM index with its parametric counterpart. Finally, we apply our approach to estimate inequality aversion in European countries.