International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Economic inequality measures are employed as a key component in various socio-demographic indices to capture the disparity between the wealthy and poor. Since their inception, they have also been used as a basis for modelling spread and disparity in other contexts. While recent research has identified that a number of classical inequality and welfare functions can be considered in the framework of OWA operators, here we propose a framework of penalty-based aggregation functions and their associated penalties as measures of inequality.

It is unanimously recognised in the literature that the concept of Quality of Life should be measured within a multidimensional framework, that is able to add to the information usually provided by indices based on economic variables. This paper proposes to adopt a new brand approach for the measurement of quality of life, which is based on the so called fuzzy set approach, and for the first time implement it in a comparative context. The empirical analysis is based on the third wave of European Quality of Life Survey, conducted in 2012 by Eurofound. The fuzzy set approach to Quality of Life measurement, results to be consistent when compared to the traditional approach defined by Eurofound; moreover, it results to also statistically robust. In conclusion, the fuzzy set approach provides quite significant added value for both data users and data analysts since it presents results which are easy to read, are concise, and it also facilitates comparison among dimensions.

In recent years there has been an increasing interest in the measurement of well-being of individuals and societies. Influenced by the “beyond GDP” initiative, in 2012 the Italian National Institute of Statistics (ISTAT) and the National Council for Economics and Labour launched the Equitable and Sustainable Well-being (BES, from the Italian acronym of “Benessere Equo e Sostenibile”) project, a set of 134 indicators aimed at capturing the Italian well-being. Lately, the debate on how to measure the well-being moved from the national level to the local one. Following this new trend, ISTAT introduced a set of 88 indicators for the local well-being (at NUTS3 level), the so called “Provinces’ BES”. Based on this project, aim of the paper is to provide an exploratory analysis for detecting groups of Italian provinces that share similar well-being profiles. In particular, we first apply a factor analysis with the aim to reduce the high number of indicators and, grounded on these results, we then create groups of the Italian provinces, applying the cluster analysis, in order to find similarity among them. Finally, based on the result of the factor analysis, for each domain and for each Italian province, we construct a composite indicator that is a linear combination of the estimated factor scores, with weights based on the Gini index of concentration.

In this paper, we analyze the correspondence among the rankings of the Spanish regions according to different measures of monetary poverty and quality of life, in 2012. To do that, the Spearman’s rank correlation coefficient is used. Different aggregation methods are applied to calculate the selected measures of poverty and quality of life. The monetary poverty measures aggregate the income gaps, while the quality of life measures aggregate a set of indicators dealing with ten different domains. In both cases, among other traditional aggregation procedures, the exponential mean is used because its properties are especially adequate in these contexts.

Welfare is multidimensional as it involves not only income, but also education, health or labour. The composite indicators of welfare are usually based on somehow aggregating the information across dimensions and individuals. However, this approach ignores the relationship between the dimensions being aggregated. To face this goal, in this paper, we analyse the multivariate dependence between the dimensions included in the Human Development Index (HDI), namely income, health and schooling, through three copula-based measures of multivariate association: Spearman’s footrule, Gini’s gamma and Spearman’s rho. We discuss their properties and prove new results on Spearman’s footrule. The copula approach focuses on the positions of the individuals across dimensions, rather than the values that the variables attain for such individuals. Thus, it allows for more general types of dependence than the linear correlation. We base our study on data from 1980 till 2014 for the countries included in the 2015 Human Development Report. We find out that though the overall HDI has increased over this period, the dependence between its dimensions remains high and nearly unchanged, so the richest countries also tend to be the best ranked in both health and education.

In the context of the dual decomposition of the rank dependent social evaluation functions we examine the k-PTS principle introduced by Gajdos and introduce a new property with balanced sensitivity to both tails of the distribution. In particular we analyse its implications for the S-Gini family.

Inequality, asymmetry, and the median-mean ratio are related but different concepts, although they have been frequently treated as equivalent in the literature. In this paper, we find important connections between these three concepts under particular conditions. We show that the Atkinson family and the generalized entropy class of inequality indices are simple functions of the medianmean ratio when a distribution is symmetrizable by a power transformation. In such a case, the coefficient of asymmetry can be interpreted as the aversion inequality parameter of a social planner, and a social evaluation function à la Kolm-Atkinson is shown to be equivalent to median income. A social evaluation function that depends only on mean income and inequality of opportunity is found as a by-product. In addition, the Hannah-Kay family of concentration indices (of which the Herfindahl-Hirschman is a special case) is also obtained as a function of the median-mean ratio. We illustrate these results empirically using the CPS dataset for the U.S. (1992—2007) and the EU-SILC dataset for the European Union (2005–2007).