Fuzzy granulation of multi-dimensional data by a crisp double-clustering algorithm

This paper introduces a method to extract multidimensional fuzzy information granules from data, which result human understandable according to a set of formally defined properties. Specifically, a Crisp Double Clustering (CDC) algorithm is proposed, which operates as the composition of two clustering steps. First, a vector quantization algorithm is applied on the available data in order to derive a set of multidimensional prototypes. Then, multidimensional prototypes, projected on each dimension of the input space, are further clustered by a hierarchical clustering algorithm. The resulting one-dimensional prototypes are used to generate fuzzy granules that can be easy labelled so as to associate a qualitative meaning that is immediate to read and understand. The information granules so derived can be used as they are, Or can be employed as building blocks for defining human understandable fuzzy rules. The proposed method has been benchmarked on a real-world medical dataset to solve the problem of predicting a breast cancer diagnosis.