Modelling with words using Cartesian granule features

We present Cartesian granule feature, a new multidimensional feature formed over the cross product of fuzzy partition labels. Traditional fuzzy modelling approaches, mainly use flat features (one dimensional features) and, consequently suffer from decomposition error when modelling systems where there are dependencies between the input variables. Cartesian granule features help reduce (if not eliminate) the error due to the decompositional usage of features. In the approach taken here, we label the (fuzzy) subsets which partition the various universes and incorporate these labels in the form of Cartesian granules into our modelling process. Fuzzy sets defined in terms of these Cartesian granules, are extracted automatically from statistical data using the theory of mass assignments, and are incorporated into fuzzy rules. Consequently we not only compute with words, we also model with words. Due to the interpolative nature of fuzzy sets, this approach can be used to model both classification and prediction problems. Overall Cartesian granule features incorporated into fuzzy rules yield glass-box models and when demonstrated on the ellipse classification problem yields a classification accuracy of 98%, outperforming standard modelling approaches such as neural networks and the data browser