Defining the poverty line has been acknowledged as being highly variable by the majority of published literature. Despite long discussions and successes, poverty line has a number of problems due to its arbitrary nature. This paper proposes three measurements of poverty lines using membership functions based on fuzzy set theory. The three membership functions, namely exponential, trapezoidal and quadratic sigmoid together with their calculation steps are discussed. Average monthly household incomes of Malaysians are used to illustrate the proposed poverty line. Three new sets of poverty lines were derived for 3 years as numerical application to the proposed membership functions. The numerical results show the flexibility of poverty lines resulted from the composition of the proposed functions. It suggests that the official poverty line for Malaysians is too low thus creating an underestimation of the extent of poverty in Malaysia.