Abstract
In this paper, a multi-objective constrained optimization model is proposed to improve interpretability of TSK fuzzy models. This approach allows a linguistic approximation of the fuzzy models. A multi-objective evolutionary algorithm is implemented with three different selection and generational replacements schemata (Niched Preselection, NSGA-II and ENORA) to generate fuzzy models in the proposed optimization context. The results clearly show a real ability and effectiveness of the proposed approach to find accurate and interpretable TSK fuzzy models. These schemata have been compared in terms of accuracy, interpretability and compactness by using three test problems studied in literature. Statistical tests have also been used with optimality and diversity multi-objective metrics to compare the schemata.
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References
Babuska, R., Verbruggen, H.B.: Applied fuzzy modeling. In: IFAC Symposium on Artificial Intelligence in Real time Control, Valencia, Spain, pp. 61–68 (1994)
Casillas, J., Cordón, O., Herrera, F., Magdalena, L.: Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview. In: Casillas, J., Cordón, O., Herrera, F., Magdalena, L. (eds.) Interpretability Issues in Fuzzy Modeling, Studies in Fuzziness and Soft Computing, pp. 3–22. Springer, Heidelberg (2003)
Coello, C.A., Veldhuizen, D.V., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic/Plenum publishers, New York (2002)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley and Sons, Ltd, Chichester (2001)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)
Gómez-Skarmeta, A.F., Jiménez, F.: Fuzzy modeling with hybrid systems. Fuzzy Sets and Systems 104, 199–208 (1999)
Gómez-Skarmeta, A.F., Jiménez, F., Sánchez, G.: Improving Interpretability in Approximative Fuzzy Models via Multiobjective Evolutionary Algorithms. International Journal of Intelligent Systems 22, 943–969 (2007)
Ishibuchi, H., Murata, T., Türksen, I.: Single-objective and two-objective genetic algorithms for selecting linguistic rules for pattern classification problems. Fuzzy Sets and Systems 89, 135–150 (1997)
Ishibuchi, H., Nakashima, T., Murata, T.: Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems. IEEE Transactions on Systems, Man, and Cubernetics - Part B: Cybernetics 29(5), 601–618 (1999)
Jiménez, F., Gómez-Skarmeta, A.F., Sánchez, G., Deb, K.: An evolutionary algorithm for constrained multi-objective optimization. In: Proceedings IEEE World Congress on Evolutionary Computation (2002)
Russo, M.: FuGeNeSys - a fuzzy genetic neural system for fuzzy modeling. IEEE Transactions on Fuzzy Systems 6(3), 373–388 (1998)
Sánchez, G., Jiménez, J., Vasant, P.: Fuzzy Optimization with Multi-Objective Evolutionary Algorithms: a Case Study. In: IEEE Symposium of Computational Intelligence in Multicriteria Decision Making (MCDM), Honolulu, Hawaii (2007)
Setnes, M.: Fuzzy Rule Base Simplification Using Similarity Measures. M.Sc. thesis, Delft University of Technology, Delft, the Netherlands (1995)
Setnes, M., Babuska, R., Verbruggen, H.B.: Rule-based modeling: Precision and transparency. IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications & Reviews 28, 165–169 (1998)
Sugeno, M., Kang, G.T.: Structure identification of fuzzy model. Fuzzy Sets and Systems 28, 15–23 (1998)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on Systems, Man and Cybernetics 15, 116–132 (1985)
Valente de Oliveira, J.: Semantic constraints for membership function optimization. IEEE Transactions on Fuzzy Systems 19(1), 128–138 (1999)
Wang, L., Yen, J.: Extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and Kalman filter. Fuzzy Sets and Systems 101, 353–362 (1999)
Yen, J., Wang, L.: Application of statistical information criteria for optimal fuzzy model construction. IEEE Transactions on Fuzzy Systems 6(3), 362–371 (1998)
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Sánchez, G., Jiménez, F., Sánchez, J.F., Alcaraz, J.M. (2010). A Multi-objective Neuro-evolutionary Algorithm to Obtain Interpretable Fuzzy Models. In: Meseguer, P., Mandow, L., Gasca, R.M. (eds) Current Topics in Artificial Intelligence. CAEPIA 2009. Lecture Notes in Computer Science(), vol 5988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14264-2_6
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DOI: https://doi.org/10.1007/978-3-642-14264-2_6
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