An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets

Multidimensional poverty concentrates on deprivations in the living standard of a population in terms of functioning failures of different quality of life attributes such as per capita real GDP, life expectancy at birth and educational attainment. More precisely, a threshold level is specified for each attribute and shortfalls of quantities of different attributes from respective thresholds for different individuals are aggregated into an overall indicator of poverty. However, there may be cases in which one is unable to determine precisely the status of a person with respect to an attribute, that is, whether he is poor or non-poor. Since the theory of fuzzy sets enables us to talk of imprecisions in a meaningful way, this paper makes an attempt to extend multidimensional poverty measurement to a fuzzy environment. Suitable fuzzy analogues are proposed for various standard index properties. Possible fuzzy indices associated with some multidimensional poverty indices are also proposed.