Credit risk profiling using a new evaluation of interval-valued fuzzy sets based on alpha-cuts

In this paper we propose a parametric way to associate to an interval-valued fuzzy set its evaluation useful for its ranking. The novelty of this paper is connected with the fact that we follow a line based on its α-cuts and the parametric formulation we obtain, leaves to the decision maker a wide freedom. For particular values of these parameters we obtain Nie and Tan defuzzification method that, in its classical definition, shows only the evaluation, but looking at it in this new version we obtain further information. The proposed methodology is then applied to risk profiling of a bank client using an interval type-2 fuzzy logic system.