Annarita Fanizzi

Homogenous Urban Poverty Clusters within the City of Bari

This work aims to determine homogenous urban poverty clusterswithin the City of Bari based on the most recent available data released by ISTAT (Italian National Statistics Institute) in the last General Population and Residential Census (2001). In particular, techniques of fuzzy grouping have been used in order to better compare the different clusters. The use of thesetechniques makes it possible to determine three different groupings of census sections, which are sufficiently homogenous in themselves and heterogeneous with each other in terms of urban poverty.

A Fuzzy Approach to the Small Area Estimation of Poverty in Italy

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.

A fuzzy approach to discriminant analysis based on polynomial regression models

The dissimilarity among the combined units in common classification techniques leads to consider the opportunity of assigning each of them to more than a single group with different degrees of membership. In this paper, we propose a discriminant analysis structured by regressing such degrees on the classification variables. In particular, we show that even the sum of the estimated degrees of membership equals one for every unit. Polynomial regression models are actually more appropriate than linear ones, as the rate of increase or decrease of each dependent variable can vary depending on the values assumed by the independent variables; the order of the polynomial is to be chosen so as to ensure both the homogeneity within clusters and the parsimony of the entire regression model. The reliability of our proposal is showed in an applicative case, concerning the entrepreneurial propensity of the provinces in Central and Southern Italy.

A Fuzzy Approach to Ward’s Method of Classification: An Application Case to the Italian University System

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. [This work is the result of joint reflections by the authors, with the following contributions attributed to Campobasso (Sects. 2.2, 2.3.2 and 2.4), and to Fanizzi (Sects. 2.1, 2.3 and 2.3.1).]

The Pricing of Risky Securities in a Fuzzy Least Square Regression Model

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.

A Proposal for a Discriminant Analysis Based on the Results of a Preliminary Fuzzy Clustering

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. The same logic can be applied in attributing a new observation to previously identified fuzzy groups. This paper precisely presents a proposal for a discriminant analysis, structured by regressing the degrees of membership to every groups of each unit on the same variables used in a preliminary clustering. Such a proposal, initially conceived to assign new customers to defined groups for Customer Relationship Management (CRM) purposes, is now tested in an applicative case concerning the entrepreneurial propensity of the sampled provinces of Central and Southern Italy, in which an iterative fuzzy k-means method is preliminary used to split them into an optimal number of homogeneous groups.

Goodness of Fit Measures and Model Selection in a Fuzzy Least Squares Regression Analysis

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.

The Graduates’ Satisfaction at Work Through a Generalization of the Fuzzy Least Square Regression Model

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.

A proposal for a stepwise fuzzy regression: an application to the italian university system

Fuzzy regression techniques can be used to fit fuzzy data into a regression analysis. Diamond treated the case of a simple least square model introducing a metrics into the space of triangular fuzzy numbers; in this paper we propose a stepwise procedure to select independent variables in a multivariate model. At each iteration we introduce into the equation the variable which is less correlated with the already present ones and, at the same time, significantly explains the total sum of the squares of the estimated model; in any case a variable, whose explanatory contribution is subrogated by the combination of those later introduced, can be eliminated until the end of the iterations. The goodness of the proposed selection procedure is reviewed in the evaluative context of the Italian university system. In our country educational offer has been recently enriched of innovative services, such as those directed to information for students and, more specifically, to their input or output guidance; as an example, teaching regulations recently allow students to gain a training experience directly in workplaces. In the perspective of monitoring more closely the innovative services offered by universities, we evaluate the effectiveness of the activated internships through the opinion (itself fuzzy) expressed by students on many aspects concerning them.