Quality of measures for attribute selection in fuzzy decision trees

In this paper, a hierarchical model of functions is presented to study and to validate functions used in an inductive learning process as measures of discrimination. This model is a fuzzy extension of a previously introduced model based on the use of any t-norm to value the intersection of fuzzy sets. Moreover, this model is based on the classically used definition of the inclusion of fuzzy sets. By means of this model, three well-known measures used to select attributes during the construction of a fuzzy decision tree are shown well-adapted as measures of discrimination. However, it is also shown that the use of an extension of the entropy of fuzzy events based on the use of Zadeh´s t-norm is not convenient for such a process.