Generation of Interpretable Fuzzy Granules by a Double-Clustering Technique

This paper proposes an approach to derive fuzzy granules from numerical data. Granules are first formed by means of a double- clustering technique, and then properly fuzzified so as to obtain interpretable granules, in the sense that they can be described by linguistic labels. The double-clustering technique involves two steps. First, information granules are induced in the space of numerical data via the FCM algorithm. In the second step, the prototypes obtained in the first step are further clustered along each dimension via a hierarchical clustering, in order to obtain one- dimensional granules that are afterwards quantified as fuzzy sets. The derived fuzzy sets can be used as building blocks of a fuzzy rule-based model. The approach is illustrated with the aid of a benchmark classification example that provides insight into the interpretability of the induced granules and their effect on the results of classification.