A new class of fuzzy poverty measures

Abstract

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.

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“…In order to quantitatively capture the mentioned dendrogram skewness, we may refer to the definition of an inequity (economic inequality, poverty) index, compare [2,8,24] and, e.g., [35,36] for a different setting.…”

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“…It is recognized that a standard summary of wages cannot capture the economic situation of a community with individuals having a range of incomes I , so some indices also incorporate the extent to which the incomes of individuals/households are below the poverty line 29 , the difference in incomes, or sometimes even the gap between male and female wages (e.g. 47 ).…”