A new fuzzy unidimensional poverty index from an information theory perspective

Abstract

Poverty, Poverty line, Fuzzy sets, Membership function, Information function, P46, I32, D81, C00,

A new class of fuzzy poverty measures

“…, n}, and by x > y we mean x ≥ y and x = y. Given x ∈ [0, ∞) n , the increasing and decreasing reorderings of the coordinates of x are indicated as [1] . Clearly,…”

“…Following Cerioli and Zani [6] and Chakravarty [9], two poverty lines should be fixed 1 . Thus, incomes can be sorted into three types: extreme poverty, moderate poverty and non-poverty, whenever incomes are below the smaller poverty line, between both poverty lines or above the highest poverty line, respectively.…”

“…The membership function of incomes to poverty assigns 1 to extreme poverty, 0 to non-poverty, and intermediate values to moderate poverty, through a continuous and decreasing function. Other contributions of poverty measurement within the fuzzy approach can be found in Shorrocks and Subramanian [29], Chiappero-Martinetti [11], Qizilbash [26], Subramanian [30], Belhadj [1,2], Belhadj and Limam [3] and Zheng [33], among others.…”

Eficacia de la política contra la pobreza en la UE. Evaluación con el "Fuzzy Pverty Indicator" (FPI)

“…Entre estos estudios, hay algunos que incorporan contribuciones adicionales aplicadas a hacer frente a la complejidad del estudio multidimensional de la pobreza (Martinetti, 2000), otros que profundizan en la medición de la pobreza con la técnica de los conjuntos difusos (Belhadj, 2011; Alkire y Foster, 2011;Miceli, 1998), y otros de carác-ter aplicado, donde se analiza la pobreza en países tan dispares como Túnez (Belhadj y Matoussi, 2010), Italia (Cheli y Betti, 1999; Dagum y Costa, 2004) o Sudáfrica (Qizilbash, 2002), entre otros.…”

“…This technique, which successfully combines a series of methods used for a multidimensional measurement of poverty 1 , has, since Cerioli and Zani (1990) introduced it for that aim, been used in a number of academic studies, both for a multidimensional and one-dimensional explanation of the phenomenon of the risk of poverty. Among these studies, there are some that incorporate additional contributions, applied to address the complexity of the multidimensional study of poverty (Marinetti, 2000), others that measure poverty more in depth using the fuzzy set technique (Belhadj , 2011;Alkire and Foster, 2011;Miceli, 1998), and other applied studies in which poverty is analysed in countries as diverse as Tunisia (Belhadj and Matoussi, 2010), Italy (Cheli and Betti, 1999;Dagum and Costa, 2004) and South Africa (Qizilbash, 2002), among others.…”