Visualizing high dimensional fuzzy rules

In this paper we present an approach to visualize a potentially high-dimensional and large number of (fuzzy) rules in two dimensions. This visualization presents the entire set of rules to the user as one coherent picture. We use a gradient descent based algorithm to generate a 2D-view of the rule set which minimizes the error on the pair-wise fuzzy distances between all rules. This approach is superior to a simple projection and also most non-linear transformations in that it concentrates on the important feature, that is the inter-point distances. In order to make use of the uncertain nature of the underlying fuzzy rules, a new fuzzy distance-measure was developed. The visualizations of a rule set for the well-known IRIS dataset as well as fuzzy models for other benchmark data sets are illustrated and discussed.