# Multi-objective genetic learning of serial hierarchical fuzzy systems for large-scale problems

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## Abstract

When we face a problem with a high number of variables using a standard fuzzy system, the number of rules increases exponentially and the obtained fuzzy system is scarcely interpretable. This problem can be handled by arranging the inputs in hierarchical ways. This paper presents a multi-objective genetic algorithm that learns serial hierarchical fuzzy systems with the aim of coping with the curse of dimensionality. By means of an experimental study, we have observed that our algorithm obtains good results in interpretability and accuracy with problems in which the number of variables is relatively high.

## Keywords

Curse of dimensionality Hierarchical fuzzy systems Multi-objective genetic algorithms Variable selection## Notes

### Acknowledgments

The authors would like to thank Astrophysics Institute of Andalusia (IAA) and Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) [both from the Spanish National Research Council (CSIC)] for providing us with the Grid nodes used to obtain the experimental results. This work was supported in part by the Spanish Ministry of Science and Innovation (Grant No. TIN2011-28488), the Spanish National Research Council (Grant No. 200450E494), and the Andalusian Government (Grant Nos. P07-TIC-3185 and TIC-2010-6858).

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