Urban poverty, especially in metropolitan areas, represents one of the most significant problems to both developed and developing countries. The aim of the present work is to identify territorial zones characterized by the presence of such a phenomenon. In particular, data gathered from the EU-SILC study for 2006 has been examined and elaborated in order to obtain estimates of poverty at a provincial level through the use of statistical methods such as Small Area Estimation and Total Fuzzy and Relative. The results obtained from this approach have been improved using SaTScan methodology for the graphical identification of homogeneous areas of poverty.

The common classification techniques are designed for a rigid (even if probabilistic) allocation of each unit into one of several groups. Nevertheless the dissimilarity among combined units often leads to consider the opportunity of assigning each of them to more than a single group with different degrees of membership. In previous works we proposed a fuzzy approach to discriminant analysis, structured by linearly regressing the degrees of membership of each unit to every groups on the same variables used in a preliminary clustering. In this work we show that non-linear regression models can be used more profitably than linear ones. The applicative case concerns the entrepreneurial propensity of provinces in Central and Southern Italy, even if our methodological proposal was initially conceived to assign new customers to defined groups for Customer Relationship Management (CRM) purposes.

A great part of statistical techniques has been thought for exact numerical data, although available information is often imprecise, partial, or not expressed in truly numerical terms. In these cases the use of fuzzy numbers can be seen as an appropriate way for a more effective representation of observed data. Diamond introduced a metrics into the space of triangular fuzzy numbers in the context of a simple linear regression model; in this work we suggest a multivariate generalization of such a distance between trapezoidal fuzzy numbers to be used in clustering techniques. As an application case of the proposed measure of dissimilarity, we identify homogeneous groups of Italian universities according to graduates’ opinion (itself fuzzy) on many aspects concerning internship activities, by disciplinary area of teaching. Since such an opinion depends not only on the quality of internships, but also on the local context within which the activity is carried out, the obtained clusters are analyzed paying attention particularly to the membership of each university to Northern, Central, or Southern Italy.

Numerous epidemiological studies based on time-series analysis have shown associations between morbidity/mortality caused by respiratory and cardiovascular adverse events and chronic exposure to airborne particles (Bell et al. 2004), but a considerable uncertainty remains to be seen. This begs the question of whether these associations represent premature morbidity within only a few days among those people already near to acute health events. Statistical aspects of such a displacement effect (or harvesting) have been discussed by several authors (Dominici et al. 2003 and references therein); a reasonable underlying hypothesis is that mortality/morbidity displacement is associated with shorter timescales, while longer time scales are supposed to be resistant to displacement. If associations reflect only harvesting, the effect of air pollution on morbidity can be considered as having a limited impact from a public-health point of view. In this paper we discuss a new approach to assess the effect of short term changes in air pollution on acute health effects. Our method is based on a Singular Spectrum Analysis (SSA) decomposition of airborne particulate matter time series into a set of exposure variable, each one representing a different timescale. An advantage of our approach is that timescales need not to be set prior to their estimation.

Over recent years, and related in particular to the significant recent international economic crisis, an increasingly worrying rise in poverty levels has been observed both in Italy, as well as in other countries. Such a phenomenon may be analysed from an objective perspective (i.e. in relation to the macro and micro-economic causes by which it is determined) or, rather, from a subjective perspective (i.e. taking into consideration the point of view of individuals or families who locate themselves as being in a condition of hardship). Indeed, the individual “perception” of a state of being allows for the identification of measures of poverty levels to a much greater degree than would the assessment of an external observer. For this reason, experts in the field have, in recent years, attempted to overcome the limitations of traditional approaches, focusing instead on a multidimensional approach towards social and economic hardship, equipping themselves with a wide range of indicators on living conditions, whilst simultaneously adopting mathematical tools which allow for a satisfactory investigation of the complexity of the phenomenon under examination. The present work elaborates on data revealed by the EUSILC survey of 2006 regarding the perception of poverty by Italian families, through a fuzzy regression model, with the aim of identifying the most relevant factors over others in influencing such perceptions.

Market researches and opinion polls usually include customers’ responses as verbal labels of sets with vague and uncertain borders. Recently we generalized the estimation procedure of a simple regression model with triangular fuzzy numbers, into the space of which Diamond introduced a metrics, to the case of a multivariate model with an asymmetric intercept also fuzzy. In this paper we show under what conditions the sum of squares of the de-pendent variable can be decomposed in exactly the same way as the classical OLS estimation and we propose a fuzzy version of the coefficient of determination, which takes into account the corresponding freedom degrees. Furthermore we introduce a stepwise procedure designed not only to include only one inde-pendent variable at a time, but also to eliminate in each iteration that variable whose explanatory contribution is subrogated by the combination of the other ones included after it was.

La metodologia di analisi cosiddetta "Total Fuzzy and Relative" utilizza, per l’appunto, la tecnica degli insiemi sfocati per ottenere una misura di incidenza di povertà relativa nell’ambito di una popolazione, a partire dall’informazione statistica fornita da una pluralità di indicatori (Lemmi e Pannuzi, 1995). Sulla scorta di tale metodologia, con il presente lavoro si cerca di identificare zone a rischio (hot spots) tra le diverse province italiane, utilizzando indicatori di disagio socio-abitativo che consentano di determinarne il relativo grado di povertà (Montrone, Perchinunno, Torre, 2007).

In previous works we provided some theoretical results on the estimates of a fuzzy linear regression model. In this paper we propose a generalization of such results to a polynomial model with multiplicative factors, which is actually more appropriate than the linear one. In fact, even in a fuzzy approach the growth rate of the dependent variable can vary depending on the values assumed by independent variables as well as on their interaction. In this application case, we regress the overall satisfaction for the working experience, expressed by the second cycle graduates in the 2008 of the University of Bari, on their satisfaction for specific aspects of job. Since the interviewed graduates express their own liking through scores which do not represent an objective measure of the personal opinions, but rather correspond to accumulation values on the submitted scale, the fuzzy approach is adequate to deal with such collected data.

This work aims to estimate the relationship between the expected return of a financial investment and its risk by means of a fuzzy version of the Capital Asset Pricing Model (CAPM). The expected return is usually computed as a function both of the rate of a risk-free security, that represents the time value of money, and of a premium that compensates investors for taking on an additional risk in the market. Actually we estimate the parameters of a simple regression model, where the dependent variable consists in the percentage change in prices of a surveyed (stable or volatile) stock and the independent variable consists in the percentage change in market indexes. As both changes in closure prices only partially represent the actual trend in returns, we use a range of observed values for each price; this allows us to estimate the sensitiveness of the stock to risk by means of the so called Fuzzy Least Square Regression. The corresponding estimates are compared with the ones obtained by means of the Ordinary Least Square Regression.