Logic-based granular prototyping

A fuzzy logic based similarity measure is introduced as a criterion for the identification of structure in data. An important characteristic of the proposed approach is that cluster prototypes are formed and evaluated in the course of the optimization without any a-priori assumptions about the number of clusters. The intuitively straightforward compound optimization criterion of maximizing the overall similarity between data and the prototypes while minimizing the similarity between the prototypes has been adopted. It is shown that the partitioning of the pattern space obtained in the course of the optimization is more intuitive than the one obtained for the standard FCM. The local properties of clusters (in terms of the ranking order of features in the multi-dimensional pattern space) are captured by the weight vector associated with each cluster prototype. The weight vector is then used for the construction of interpretable information granules.