Fuzzy conceptualization of privation has been a step closer to more realistic handling of poverty. However, fuzzy approaches to poverty are still grounded on parametric axioms. Moreover, construction of poverty lines within these approaches still relies on ad‐hoc methods. In this paper, we advance instead a fuzzy procedure based on the non‐parametric bootstrap method, allowing us to depict fuzzy unidimensional privation states with boundaries drawn spontaneously from data. Fuzzy non‐parametric measures of privation within each state as well as a collective fuzzy non‐parametric index of poverty are derived, along with their corresponding confidence intervals. The new approach is applied to the analysis of poverty in Tunisia in 2005.