Analyzing Borders Between Partially Contradicting Fuzzy Classification Rules

Fuzzy classification rules allow the definition of readable and interpretable rule bases. Nevertheless, the shape of the resulting class borders of fuzzy classification rules depends to a great part on the used tnorm and t-conorm and can sometimes even be counter-intuitive. In this paper we discuss the shape of class borders between overlapping rules under consideration of different t-norms and t-conorms and the effect of rule aggregation, i.e. more than one rule defining the same class are overlapping. Furthermore, we discuss the influence of rule weights and point out some aspects of the classification behavior of naive Bayes classifiers, which can be seen as a subset of fuzzy systems. Our main goal is to give the potential user an insight into the classification behavior of fuzzy classifiers. For this, mainly 2D and 3D visualizations are used to illustrate the cluster shapes and the borders between distinct classes.