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

Abstract

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).]