Input features' impact on fuzzy decision processes

Many real-world applications have very high dimensionality and require very complex decision borders. In this case, the number of fuzzy rules can proliferate, and the easy interpretability of fuzzy models can progressively disappear. An important part of the model interpretation lies on the evaluation of the effectiveness of the input features on the decision process. In this paper, we present a method that quantifies the discriminative power of the input features in a fuzzy model. The separability among all the rules of the fuzzy model produces a measure of the information available in the system. Such measure of information is calculated to characterize the system before and after each input feature is used for classification. The resulting information gain quantifies the discriminative power of that input feature. The comparison among the information gains of the different input features can yield better insights into the selected fuzzy classification strategy, even for very high dimensional cases, and can lead to a possible reduction of the input space dimension. Several artificial and real-world data analysis scenarios are reported as examples in order to illustrate the characteristics and potentialities of the proposed method.