Interpretable fuzzy partitioning of classified data with variable granularity

Fuzzy rule-based systems are effective tools for acquiring knowledge from data and represent it in a linguistically interpretable form. To achieve interpretability, input features are granulated in fuzzy partitions. A critical design decision is the selection of the granularity level for each input feature. This paper presents an approach, called DC* (Double Clustering with A*), for automatically designing interpretable fuzzy partitions with optimal granularity. DC* is specific for classification problems and is mainly based on a two-stage process: the first stage identifies clusters of multidimensional samples in order to derive class-labeled prototypes; in the second stage the one-dimensional projections of such prototypes are further clustered along each dimension simultaneously, thus minimizing the number of clusters for each feature. Moreover, the resulting one-dimensional clusters provide information to define fuzzy partitions that satisfy a number of interpretability constraints and exhibit variable granularity levels. The fuzzy sets in each partition can be labeled by meaningful linguistic terms and used to represent knowledge in a natural language form. Experimental results on both synthetic and real data show that the derived fuzzy partitions can be exploited to define very compact fuzzy rule-based systems that exhibit high linguistic interpretability and good classification accuracy.