Page 212 - Contributed Paper Session (CPS) - Volume 4

CPS2192 Laurent D. et al.

Fuzzy individual and global assessments, and
FANOVA. Application: Fuzzy measure of poverty
with Swiss data
Laurent Donzé, Rédina Berkachy
Applied Statistics and Modelling, Department of Informatics, University of Fribourg,
Switzerland

Abstract
The measure of poverty is an excellent field to apply fuzzy statistics. Indeed,
nowadays, this measure is fast always considered as multidimensional.
Furthermore, the evaluation of a poverty level, which is on a large scale
subjective and varying between individuals and upon situations, has
undoubtfully a fuzzy content. We propose, first, to show in a fuzzy approach
how individual and global assessments can be implemented. Second, we
develop a fuzzy ANOVA method. We use then these two theoretical tools in
order to evaluate the level of poverty, concerning financial conditions, in
Switzerland. We test the difference in poverty between two groups of
population, Swiss and foreigners.

Keywords
Fuzzy Statistics; Signed Distance; FANOVA; Linguistic Questionnaire; Poverty
Measure

1. Introduction
The measure of poverty has challenged the economists and statisticians
during decades. It appears that nowadays the measure has to be
multidimensional, in the sense that several factors impacting the poverty have
to be taking into account. Whatever the measure considered, the problem of
evaluating the level of poverty remains. This task is mainly subjective and
generally depends on personal considerations. Regarding this latter point,
which shows that imprecision and vagueness could be essential, we propose
to model the measure of poverty by a fuzzy approach. Indeed, we are not the
first to advocate such a modelisation, and for instance we can cite Belhadj
(2011), Belhadj and Limam (2012), Chatterjee, Mukherjee, and Kar (2014),
Miceli (1998), and Mussard and Pi Alperin (2005).
On another side, the surveys intending to capture the poverty level in a
given population, for example, those produced by national statistical offices,
are mainly conceived as linguistic questionnaires. The proper evaluation of
such questionnaires becomes thus a priority in producing meaningful poverty
indices. In some former works, we showed how to implement fuzzy individual
and global evaluations of linguistic questionnaires. We also demonstrated

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