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Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems

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Abstract

Recently, multi-objective evolutionary algorithms have been applied to improve the difficult tradeoff between interpretability and accuracy of fuzzy rule-based systems. It is known that both requirements are usually contradictory, however, these kinds of algorithms can obtain a set of solutions with different trade-offs. This contribution analyzes different application alternatives in order to attain the desired accuracy/interpr-etability balance by maintaining the improved accuracy that a tuning of membership functions could give but trying to obtain more compact models. In this way, we propose the use of multi-objective evolutionary algorithms as a tool to get almost one improved solution with respect to a classic single objective approach (a solution that could dominate the one obtained by such algorithm in terms of the system error and number of rules). To do that, this work presents and analyzes the application of six different multi-objective evolutionary algorithms to obtain simpler and still accurate linguistic fuzzy models by performing rule selection and a tuning of the membership functions. The results on two different scenarios show that the use of expert knowledge in the algorithm design process significantly improves the search ability of these algorithms and that they are able to improve both objectives together, obtaining more accurate and at the same time simpler models with respect to the single objective based approach.

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Notes

  1. With these values we have tried to ease the comparisons selecting standard common parameters that work well in most cases instead of searching for very specific values to each method. Moreover, we have set a large number of evaluations in order to allow the compared algorithms to achieve an appropriate convergence.

  2. These data sets are available at: http://decsai.ugr.es/∼casillas/fmlib.

  3. Available from the UCI Machine Learning Repository (http://www.ics.uci.edu/∼mlearn/MLRepository.html).

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Acknowledgment

Supported in part by the Spanish Ministry of Education and Science under grant no. TIN2005-08386-C05-01, and the Andalusian government under grant no. P05-TIC-00531.

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Authors and Affiliations

  1. Department of Computer Science and A.I, University of Granada, Granada, 18071, Spain

    María José Gacto, Rafael Alcalá & Francisco Herrera

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  1. María José Gacto
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  2. Rafael Alcalá
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  3. Francisco Herrera
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Correspondence to María José Gacto.

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Gacto, M.J., Alcalá, R. & Herrera, F. Adaptation and application of multi-objective evolutionary algorithms for rule reduction and parameter tuning of fuzzy rule-based systems. Soft Comput 13, 419–436 (2009). https://doi.org/10.1007/s00500-008-0359-z

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