Piecewise-Linear Approximation of Nonlinear Models Based on Interval Numbers (INs)

Linear models are ususally preferable due to their simplicity. However, nonlinear models often emerge in practice. A popular approach for dealing with nonlinearities is using a piecewise-linear approximation. In such context, inspired from both Fuzzy Inference Systems (FISs) of TSK type and Self-Organizing Maps (SOMs), this work introduces enhancements based on Interval Numbers and, ultimately, on lattice theory. Advantages include a capacity to deal with granular inputs, introduction of tunable nonlinearities, representation of all-order statistics, and induction of descriptive decision-making knowledge (rules) from the training data. Preliminary computational experiments here demonstrate a good capacity for generalization; furthermore, only a few rules are induced.