Gini Coefficient for Fuzzy Data

Document Type : Original Article

Author

20.1001.1.27174409.1399.3.2.3.0/DOR

Abstract

Poverty and inequality is one of the great problems that human societies have faced throughout history. Hence, one of the most important goals of world governments is to reduce poverty and inequality. Gini coefficient is one of the most common and widely used indicators for measuring economic inequality. Since much of the actual data on individuals' income and expenditure may be inaccurate, it seems necessary to expand the concept of Gini coefficient in a fuzzy environment. In this paper, we examine the Gini coefficient based on fuzzy observations. In the end, the presented methods are described using a real example.

Keywords


[1] سرگلزائی, شکوه, حسین زاده سلجوقی, فرانک, آقایاری, هادی. (1397) ارائه روشی نوین برای رتبه بندی اعداد فازی با استفاده از مرکز محیطی دایره و کاربرد آن در ارزیابی عملکرد مدیریت زنجیره تأمین. تصمیم گیری و تحقیق در عملیات. دوره 3، شماره (3):صص236-48.
 
[2] طاهری، محمود، ماشین چی، ماشالله. مقدمه‌ای بر احتمال و آمار فازی. (1392). انتشارات دانشگاه شهید باهنر کرمان.
 
[3] Adamo.M. (1980). Fuzzy decision trees, Fuzzy Sets and Systems, 4, 207–219.
 
[4] Anand, S. (1983). Inequality and Poverty in Malaysia: Measurement and Decomposition. New York: Oxford University Press.
 
[5] Campos. L and Munoz. A. (1989). A subjective approach for ranking fuzzy numbers, Fuzzy Sets and Systems. 29. 145-153.
 
[6] Chakravarty, S. R. (1990). Ethical Social Index Numbers, Berlin: Springer-Verlag.
 
[7] Chang, W. Ranking of fuzzy utilities with triangular membership functions.(1999). Fuzzy Sets and Systems, 105.365-375.
 
[8] Chen, C. H. (1998). A new approach for ranking fuzzy numbers by distance method, fuzzy sets and system, 959,(3). 307-317.
 
[9] Chu, T. C., and Tsao, C. T. (2002). Ranking fuzzy numbers with an area between the centroid point and original point. Computers & mathematics with applications, 43(1-2), 111-117.
 
[10] de Campos Ibáñez, L. M., and Muñoz, A. G. (1989). A subjective approach for ranking fuzzy numbers. Fuzzy sets and systems, 29(2), 145-153.
 
[11] Gini, C. (1912), Variability and mutability, contribution to the study of statistical distribution and relaitons, Studi Economico-Giuricici della R.
 
[12] Jain, R. Decision making in the presence of fuzzy variables. (1976). IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS. 6(10). 698-703.
 
[13] Kleiber, C. and Kotz, S. (2003). Statistical Size Distributions in Economics and Actuarial Ssciences, John Wiley & Sons.
 
[14] Langel, M. and Tille, Y. (2013). Variance estimation of the Gini index : revisiting a result several time published. Journal of the Royal Statistical Society -Series A, 176, 521-540.
 
[15] Wang, Z. X., Liu, Y. J., Fan, Z. P., and Feng, B. (2009). Ranking L–R fuzzy number based on deviation degree. Information sciences, 179(13), 2070-2077.
 
[16] Xu, K. (2004). How has the literature on Gini index evolved in the past 80 years?. Working Paper. Department of Economics, Dalhousie University, Halifax.
 
[17] Yager.R.R.(1978). Ranking fuzzy subsets over the unit interval, IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes,Iona College, New Rochelle, New York, 1435–1437.
 
[18] Yager.R.R. (1980). On choosing between fuzzy subsets, Kybernetes. 9, (2).151–154.
 
[19] Yitzhaki S. and Schechtman, E. (2013). The Gini Methodology: A primer on a statistical methodology. Springer Science, Business Media.
 
[20] Zadeh, L. A. (1965). Fuzzy Sets, Inform. Control, 8: 338-353.