A new class of fuzzy poverty measures

In this paper, we introduce and analyze a class of fuzzy poverty measures based on exponential means. Since poverty is a vague notion, individuals should not be classified in poor or non-poor. In our proposal, we have associated a degree of poverty to each income through a fuzzy membership function. We have extended normalized gaps from the classical approach, where poverty is a dichotomous notion, to the fuzzy setting. The proposed family of fuzzy poverty measures decomposes into the three I’s indicators: the incidence of poverty is captured through the headcount ratio, while intensity and inequality of poverty are measured by the core and the remainder, respectively, of a parameterized exponential mean over the normalized gaps of (somewhat) poor individuals. Taking into account the features of the dual decomposition of exponential means, we provide some properties of the proposed fuzzy poverty measures.

[1]  Satya R. Chakravarty,et al.  Inequality, Polarization and Poverty: Advances in Distributional Analysis , 2009 .

[2]  P. Lambert.  The Distribution and Redistribution of Income , 1989 .

[3]  R. Mesiar,et al.  Aggregation operators: properties, classes and construction methods , 2002 .

[4]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[5]  B. Zheng.  Poverty Orderings , 2000 .

[6]  B. Zheng.  Aggregate Poverty Measures , 2002 .

[7]  E. Glaeser,et al.  Inequality , 1998, Encyclopedia of the UN Sustainable Development Goals.

[8]  Mozaffar Qizilbash,et al.  Philosophical Accounts of Vagueness, Fuzzy Poverty Measures and Multidimensionality , 2006 .

[9]  Satya R. Chakravarty,et al.  Ethical Social Index Numbers , 1990 .

[10]  G. Duncan,et al.  The Perception of Poverty. , 1987 .

[11]  M. Limam,et al.  Unidimensional and multidimensional fuzzy poverty measures: New approach , 2012 .

[12]  M. Qizilbash.  Vague language and precise measurement: the case of poverty , 2003 .

[13]  José Luis García-Lapresta,et al.  A Class of Poverty Measures Induced by the Dual Decomposition of Aggregation Functions , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[14]  Mitio Nagumo.  Über eine Klasse der Mittelwerte , 1930 .

[15]  B. Cheli,et al.  A’Totally’ Fuzzy and Relative Approach to the Multidimensional Analysis of Poverty , 1995 .

[16]  Besma Belhadj,et al.  New fuzzy indices for multidimensional poverty , 2013, J. Intell. Fuzzy Syst..

[17]  R. Mesiar,et al.  Aggregation Functions: Aggregation on ordinal scales , 2009 .

[18]  José Luis García-Lapresta,et al.  The self-dual core and the anti-self-dual remainder of an aggregation operator , 2008, Fuzzy Sets Syst..

[19]  B. Belhadj.  A new fuzzy unidimensional poverty index from an information theory perspective , 2011 .

[20]  S. Zani,et al.  A Fuzzy Approach To The Measurement Of Poverty , 1990 .

[21]  Satya R. Chakravarty,et al.  An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets , 2006 .

[22]  Mariano Eriz.  Aggregation Functions: A Guide for Practitioners , 2010 .

[23]  R. Mesiar,et al.  ”Aggregation Functions”, Cambridge University Press , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[24]  A. Lemmi,et al.  Fuzzy set approach to multidimensional poverty measurement , 2006 .

[25]  E. Thorbecke,et al.  A Class of Decomposable Poverty Measures , 1984 .

[26]  A. Sen,et al.  Poverty: An Ordinal Approach to Measurement , 1976 .

[27]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[28]  E. Martinetti.  A MULTIDIMENSIONAL ASSESSMENT OF WELL-BEING BASED ON SEN ’ S FUNCTIONING APPROACH , 2000 .