Genetic tolerance fuzzy neural networks: From data to fuzzy hyperboxes

In this study, we introduce and discuss a category of genetically optimized fuzzy neural networks. As far as the underlying geometry of such networks is concerned, they are focused on revealing a hyperbox-based topology in numeric data. This class of the networks is developed around fuzzy tolerance neurons. Tolerance neurons form a generalized version of intervals (sets) arising in a form of fuzzy intervals. The architecture of the network reflects a hierarchy of geometric concepts typically exploited in data analysis: fuzzy intervals combined and-wise give rise to fuzzy hyperboxes and these in turn by being aggregated or-wise generate a summary of data as a collection of hyperboxes. We discuss a genetic form of optimization of the networks and provide an in-depth view into the geometry of the individual hyperboxes as well as the overall topology of the network. Numerical experiments deal with 2-D synthetic data.