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

摘要

The fuzzy lattice reasoning (FLR) classifier was introduced lately as an advantageous enhancement of the fuzzy-ARTMAP (FAM) neural classifier in the Euclidean space R~N. This work extends FLR to space F~N, where F 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.