# Learning consistent, complete and compact sets of fuzzy rules in conjunctive normal form for regression problems

## Abstract

When a flexible fuzzy rule structure such as those with antecedent in conjunctive normal form is used, the interpretability of the obtained fuzzy model is significantly improved. However, some important problems appear related to the interaction among this set of rules. Indeed, it is relatively easy to get inconsistencies, lack of completeness, redundancies, etc. Generally, these properties are ignored or mildly faced. This paper, however, focuses on the design of a multiobjective genetic algorithm that properly considers all these properties thus ensuring an effective search space exploration and generation of highly legible and accurate fuzzy models.

## Keywords

Genetic fuzzy systems Regression problems Multiobjective optimization Flexible fuzzy rules Interpretability constrains## Notes

### Acknowledgments

This work was supported in part by the Spanish Ministry of Education and Science under grant no. TIN2005-08386-C05-01 and the Andalusian Government under grants no. P05-TIC-00531 and P07-TIC-3185.

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