grSOM: a granular extension of the self-organizing map for structure identification applications

An extension of the self-organizing map (SOM) is presented, namely granular SOM or grSOM for short, applicable beyond R^N to F^N, where F denotes the set of fuzzy interval numbers (FINs). Rigorous analysis establishes that F is a metric mathematical lattice. A FIN is interpreted as a linguistic granule, which corresponds to a local probability distribution function. The grSOM can be used for structure identification in linguistic system modeling applications. Experimental results using the greedy grSOM algorithm compare favorably with the corresponding results by alternative algorithms from the literature in two benchmark classification problems; in addition, descriptive decision-making knowledge (fuzzy rules) is induced from the data.