Fuzzy Models
Jan Jantzen · 2013
The performance of a fuzzy rule base depends on a number of adjustable parameters, and they can be adjusted such that the rule base behaves in a more or less desired manner. In the simplest cases, a handmade model, in the shape of a rule base, suffices to approximate a curve or a surface. In more complex cases, based on measurement data, a machine-made model can approximate a function, even in many dimensions. Fuzzy rules can interpolate between local linear models in order to approximate a nonlinear function. Local linear models are conveniently built using least-squares optimization. If the partitioning into local linear models cannot be done manually, the clustering algorithms hard c-means and fuzzy c-means can point to local clusters that are candidates for a linear model. A neuro-fuzzy model is more complex - perhaps also more capable in difficult cases - and it combines the training of a neural network model with the readability of a fuzzy rule base. The result is a rule base that 'learns' the underlying function in data. The inner product is a common geometric foundation of the model architectures.