# Multiobjective genetic fuzzy rule selection of single granularity-based fuzzy classification rules and its interaction with the lateral tuning of membership functions

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## Abstract

Multiobjective genetic fuzzy rule selection is based on the generation of a set of candidate fuzzy classification rules using a preestablished granularity or multiple fuzzy partitions with different granularities for each attribute. Then, a multiobjective evolutionary algorithm is applied to perform fuzzy rule selection. Since using multiple granularities for the same attribute has been sometimes pointed out as to involve a potential interpretability loss, a mechanism to specify appropriate single granularities at the rule extraction stage has been proposed to avoid it but maintaining or even improving the classification performance. In this work, we perform a statistical study on this proposal and we extend it by combining the single granularity-based approach with a lateral tuning of the membership functions, i.e., complete contexts learning. In this way, we analyze in depth the importance of determining the appropriate contexts for learning fuzzy classifiers. To this end, we will compare the single granularity-based approach with the use of multiple granularities with and without tuning. The results show that the performance of the obtained classifiers can be even improved by obtaining the appropriate variable contexts, i.e., appropriate granularities and membership function parameters.

## Keywords

Fuzzy rule-based classifiers Multiobjective evolutionary algorithms Granularity learning Lateral tuning of membership functions## Notes

### Acknowledgments

This work was supported by the Spanish CICYT Project TIN2008-06681-C06-01 and the Japanese Grant-in-Aid for Young Scientists (B): KAKENHI (22700239).

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