Methodology and Axiomatic Characterization of a Multidimensional and Fuzzy Measure of Deprivation

This article proposes a general methodology to measure multidimensional deprivation in a fuzzy setup. Each dimension comprises multiple dimensional attributes. The methodology is developed in a flexible manner to incorporate any theoretical construct of wellbeing. The new fuzzy membership functions proposed in the method combines the absolute and relative notions of deprivation and take the functional form of normalized and weighted deprivation gaps. A new weight structure is proposed for aggregations within and across the dimensions. Three forms of deprivation indices are discussed: the headcount ratio, the adjusted deprivation index, and the deprivation index. A unified axiomatic framework is discussed for the multidimensional and fuzzy measures of deprivation. Various desired axiomatic properties of the fuzzy membership functions are included as precursory axioms in the framework. The proposed measure satisfies a majority of the desirable axioms.