Modeling uncertainty in monetary poverty: A possibility-based approach

Fuzzy sets theory has successfully accommodated the lack of clear-cut boundaries of poverty and its gradual nature. On the other hand, uncertainties related to lack of knowledge and imprecision in poverty data need also to be accounted for. The accuracy of poverty analysis is highly subject to how well these features are adequately addressed. We argue that possibility theory is an appropriate framework to deal with incomplete knowledge in poverty. Indeed, considering “the possibility of poverty” instead of the “probability of poverty” allows us to achieve a more realistic handling of this phenomenon. Empirical possibility distributions of monetary poverty states are derived based on our previous works and alpha-cut analysis is used to explore their features. Also, collective possibilistic poverty measures for each state are computed along with an aggregate possibilistic poverty ratio. This possibilistic modeling is applied to the analysis of poverty in Tunisia in 2005 and 2010.