Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this paper a multi-objective evolutionary approach is proposed to determine a Paretooptimum set of fuzzy systems with different compromises between their accuracy and complexity. In particular, two fundamental and competing objectives concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained system. Another key aspect of the algorithm presented in this work is the use of some new expert evolutionary operators, specifically designed for the problem of fuzzy function 0888-613X/$ see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.ijar.2006.02.006 q Partially supported by the Spanish Ministerio de Ciencia y Tecnologı́a under projects TIC2002–11352–E and TIN2004–01419. * Corresponding author. E-mail address: [email protected] (J. González). 1 Present address: Department of Electrotechnics and Electronics, Escuela Politécnica Superior, University of Córdoba, E–14071 Córdoba, Spain. J. González et al. / Internat. J. Approx. Reason. 44 (2007) 32–44 33 approximation, that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm. 2006 Elsevier Inc. All rights reserved.