Granular Enhancement of Fuzzy ART/SOM Neural Classifiers Based on Lattice Theory

Summary. Fuzzy adaptive resonance theory (fuzzy-ART) and self-organizing map (SOM) are two popular neural paradigms, which compute lattice-ordered granules. Hence, lattice theory emerges as a basis for unified analysis and design. We present both an enhancement of fuzzy-ART, namely fuzzy lattice reasoning (FLR), and an enhancement of SOM, namely granular SOM (grSOM). FLR as well as grSOM can rigorously deal with (fuzzy) numbers as well as with intervals. We introduce inspiring novel interpretations. In particular, the FLR is interpreted as a reasoning scheme, whereas the grSOM is interpreted as an energy function minimizer. Moreover, we can introduce tunable nonlinearities. The interest here is in classification applications. We cite evidence that the proposed techniques can clearly improve performance.

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