This paper sets out the reasoning behind the fuzzy set approach to poverty measurement as a means to address both vertical and horizontal vagueness of poverty. The linear approach of Cerioli and Zani and the totally fuzzy and relative approach of Cheli and Lemmi are discussed and applied to the Eastern Cape Province, South Africa, using data from Census 96. The results indicate different experiences of poverty in the Eastern Cape. It is shown that the traditional money metric approach does not accurately identify the most deprived in society, indicating the importance of other non-metric dimensions in poverty measurement.