Vol.:(0123456789)
Social Indicators Research
https://doi.org/10.1007/s11205-021-02681-z
1 3
ORIGINAL RESEARCH
Fuzzy Version of Gini’s Index
Besma Belhadj
1,2
· Firas Kaabi
4
· Mejda Bouanani
3
Accepted: 27 March 2021
© The Author(s), under exclusive licence to Springer Nature B.V. 2021
Abstract
The Gini index (Gini in Variabilità e mutabilità: contributo allo studio delle distribuzi-
oni e delle relazioni statistiche, Studi Economico-Giuridici, Facoltà di Giurisprudenza
della Regia Università di Cagliari, anno III, parte II, Cuppini, Bologna, 1912) is the old-
est 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 pro-
pose an axiomatic measure of inequality.
Keywords Gini’s index · Membership function of absolute equality · Membership function
of inequality · Fuzzy Gini index · Fuzzy inequaly index
JEL Classification C02 · C43 · D63
1 Introduction
The extent of income distribution within a country or group is essential (Sullivan and Ste-
ven, 2003). Income and distribution have always been a central concern of economic the-
ory and economic policy. Many economists have been concerned with the distribution of
* Besma Belhadj
besmabelhaj14@gmail.com
Firas Kaabi
firaskaabi17@gmail.com
Mejda Bouanani
mejda.bouanani@gmail.com
1
LaREQuaD, FSEGT, University of ElManar, Campus Universitaire, Tunis, Tunisia
2
LIRS, IHE Tunis, Tunis, Tunisia
3
Department of Economics and Finance, College of Business Administration, Taif University, P.O.
Box 11099, Taif 21944, Saudi Arabia
4
University of Bordeaux, Bordeaux, France