On the construction of fuzzy measures for the analysis of poverty and social exclusion
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This paper is a contribution to the analysis of deprivation seen as a multi-dimensional condition. Multi-dimensionality involves both monetary and diverse non-monetary aspects – the former as the incidence and intensity of low income, and the latter as a lack of access to other resources, facilities, social interactions and even individual attributes determining the life-style. A most useful tool for such analysis is to view deprivation as a matter of degree, giving a quantitative expression to its intensity for individuals in different dimensions and at different times. Such ‘fuzzy’ conceptualisation has been increasingly utilised in poverty and deprivation research. This paper aims to further develop and refine this strand of research, so as to integrate it in the form of a more ‘integrated fuzzy and relative’ (IFR) approach to the analysis of poverty and deprivation. The concern of the paper is primarily methodological rather than detailed numerical analysis from particular applications. We re-examine the two additional aspects introduced by the use of fuzzy (as distinct from the conventional poor/non-poor dichotomous) measures, namely: the choice of membership functions and the choice of rules for the manipulation of the resulting fuzzy sets, rules defining their complement, intersection, union and averaging. The relationship of the proposed fuzzy monetary measure with the Lorenz curve and the Gini coefficient.
Keywords: income poverty, multidimensional deprivation, fuzzy set operators. Authors biographyGianni Betti, Dipartimento di Metodi Quantitativi – Università degli Studi di Siena – P.za S. Francesco, 8, 53100 SIENA (e-mail: betti2@unisi.it).Bruno Cheli ,Dipartimento di Statistica e Matematica Applicata all'Economia – Università degli Studi di Pisa – Via C. Ridolfi, 10, 56124 PISA (e-mail: bcheli@ec.unipi.it). Achille Lemmi, Dipartimento di Metodi Quantitativi – Università degli Studi di Siena – P.za S. Francesco, 8, 53100 SIENA (e-mail: lemmi@unisi.it). Vijay Verma, Dipartimento di Metodi Quantitativi – Università degli Studi di Siena – P.za S. Francesco, 8, 53100 SIENA (e-mail:verma@unisi.it). |
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