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.