A granular extension of the fuzzy-ARTMAP (FAM) neural classifier based on fuzzy lattice reasoning (FLR)

The fuzzy lattice reasoning (FLR) classifier was introduced lately as an advantageous enhancement of the fuzzy-ARTMAP (FAM) neural classifier in the Euclidean space RNRN. This work extends FLR to space FNFN, where FF is the granular data domain of fuzzy interval numbers (FINs) including (fuzzy) numbers, intervals, and cumulative distribution functions. Based on a fundamentally improved mathematical notation this work proposes novel techniques for dealing, rigorously, with imprecision in practice. We demonstrate a favorable comparison of our proposed techniques with alternative techniques from the literature in an industrial prediction application involving digital images represented by histograms. Additional advantages of our techniques include a capacity to represent statistics of all orders by a FIN, an introduction of tunable (sigmoid) nonlinearities, a capacity for effective data processing without any data normalization, an induction of descriptive decision-making knowledge (rules) from the training data, and the potential for input variable selection.