Fuzzy Version of Gini’s Index

The Gini index (Gini in Variabilità e mutabilità: contributo allo studio delle distribuzioni e delle relazioni statistiche, Studi Economico-Giuridici, Facoltà di Giurisprudenza della Regia Università di Cagliari, anno III, parte II, Cuppini, Bologna, 1912) is the oldest and famous inequality measure. A Lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. The Gini index measures the area between the Lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line. In this paper, a fuzzy version of Gini’s index is proposed and used it to propose an axiomatic measure of inequality.