New membership function for poverty measure

Fuzziness in a fuzzy set is determined by its membership function (m.f) which translates the reality of a problem. Accordingly, the shapes of membership functions (m.fs) are important for a particular problem such as poverty since they effect on a fuzzy inference system. Some authors have used to visualize the behaviour of poverty, different shapes like triangular, trapezoidal. In this paper, a specific (m.f), named modified logistic membership function better illustrating the complicated reality, is proposed to measure poverty. The modified logistic membership function is first formulated for several states of poverty and its flexibility in taking up vagueness in poverty is established by an analytical approach using aggregate operators in order to infer a logical conclusion measuring poverty. An application based on individual well-being data from Tunisian households in 2010 is presented to illustrate use of proposed concepts.