Abstract
This chapter describes the genetic optimization of interval type-2 fuzzy integrators in Ensembles of ANFIS (adaptive neuro-fuzzy inferences systems) models for the prediction of the Mackey-Glass time series. The considered a chaotic system is he Mackey-Glass time series that is generated from the differential equations, so this benchmarks time series is used for the test of performance of the proposed ensemble architecture. We used the interval type-2 and type-1 fuzzy systems to integrate the output (forecast) of each Ensemble of ANFIS models. Genetic Algorithms (GAs) were used for the optimization of memberships function parameters of each interval type-2 fuzzy integrators. In the experiments we optimized Gaussians, Generalized Bell and Triangular membership functions for each of the fuzzy integrators, thereby increasing the complexity of the training. Simulation results show the effectiveness of the proposed approach.
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Brocklebank, J.C., Dickey, D.A.: SAS for Forecasting Series, pp. 6–140. SAS Institute Inc, Cary (2003)
Brockwell, P.D., Richard, A.D.: Introduction to Time Series and Forecasting, pp. 1–219. Springer, New York (2002)
Castillo, O., Melin, P.: Optimization of type-2 fuzzy systems based on bio-inspired methods: a concise review. Appl. Soft Comput. 12(4), 1267–1278 (2012)
Castillo, O., Melin, P.: Soft Computing for Control of Non-Linear Dynamical Systems. Springer, Heidelberg (2001)
Castro, J.R., Castillo, O., Martínez, L.G.: Interval type-2 fuzzy logic toolbox. Eng. Lett. 15(1), 89–98 (2007)
Castro, J.R., Castillo, O., Melin, P., Rodriguez, A.: A Hybrid Learning Algorithm for Interval Type-2 Fuzzy Neural Networks: The Case of Time Series Prediction, vol. 15a, pp. 363–386. Springer, Berlin (2008)
Castro, J.R., Castillo, O., Melin, P., Rodríguez, A.: Hybrid learning algorithm for interval type-2 fuzzy neural networks. In: GrC, pp. 157–162 (2007)
Chua, T.W., Tan, W.W.: Genetically evolved fuzzy rule-based classifiers and application to automotive classification. Lecture Notes in Computer Science, vol. 5361, pp. 101–110 (2008)
Cordon, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L.: Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets Syst. 141, 5–31 (2004)
Cordon, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy, Knowledge Bases. World Scientific, Singapore (2001)
Cordon, O., Herrera, F., Villar, P.: Analysis and guidelines to obtain a good uniform fuzzy partition granularity for fuzzy rule-based systems using simulated annealing. Int. J. Approximate Reasoning 25, 187–215 (2000)
Eason, G., Noble, B., Sneddon, I.N.: On certain integrals of Lipschitz-Hankel type involving products of Bessel functions. Phil. Trans. Roy. Soc. London A247, 529–551 (1995)
Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computation, pp. 37–69. Springer, Berlin (2003)
Filev, D., Yager, R.: On the issue of obtaining OWA operador weights. Fuzzy Sets Syst. 94(2), 157–169 (1998)
Goldberg, D.E., Kalyanmoy, D.: A comparative analysis of selection schemes used in genetic algorithms. In: Rawlins, G.J.E. (ed.) Foundations of Genetic Algorithms, pp. 69–93. Morgan Kaufmann Publishers, San Mateo (1991)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Boston (1989)
Goldberg, D.E., Korb, B., Kalyanmoy, D.: Messy genetic algorithms: motivation, analysis, and first results. Complex Syst. 3, 493–530 (1989)
Holland, J.H.: Outline for a logical theory of adaptive systems. J. Assoc. Comput. Mach. 3, 297–314 (1962)
Holland, J.H.: Adaptatioon in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Jang, J.S.R.: ANFIS: adaptive-network-based fuzzy inference systems. IEEE Trans. Syst. Man Cybernet. 23, 665–685 (1992)
Jang, J.S.R.: Fuzzy modeling using generalized neural networks and Kalman fliter algorithm. In: Proceedings of the Ninth National Conference on Artificial Intelligence. (AAAI-91), pp. 762–767 (1991)
Jang, J.S.R.: Rule extraction using generalized neural networks. In: Proceedings of the 4th IFSA Wolrd Congress, pp. 82–86 (1991)
Konar, A.: Computational Intelligence: Principles, Techniques and Applications. Springer, Berlin (2005)
Lawrence, D.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New Jersey (1991)
Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287–289 (1997)
Mackey, M.C.: Mackey-Glass. McGill University, Canada. http://www.sholarpedia.org/-article/ Mackey-Glass_equation, 5th Sept 2009
Melin, P., Mendoza, O., Castillo, O.: An improved method for edge detection based on interval type-2 fuzzy logic. Expert Syst. Appl. 37(12), 8527–8535 (2010)
Melin, P., Soto, J., Castillo, O., Soria, J.: Optimization of Interval Type-2 and Type-1 fuzzy integrators in ensemble of ANFIS models with genetic algorithms. In: Mexican International Conference on Computer Science, Morelia, Mexico, 30, 31 Oct–1st Nov 2013
Mendel, J.M.: Why we need type-2 fuzzy logic systems (Article is provided courtesy of Prentice Hall, By Jerry Mendel) 11 May 2001
Mendel, J.M. (ed.): Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, pp. 25–200. Prentice Hall, USA (2000)
Mendel, J.M., Mouzouris, G.C.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7, 643–658 (1999)
Michalewicz, Z.: Genetic Algorithms + Data Structures=Evolution Programs, vol. AI. Springer-Verlag, New York (1994)
Pulido, M., Melin, P., Castillo, O.: Genetic optimization of ensemble neural networks for complex time series prediction. In: Neural Networks International Joint Conference (IJCNN), pp. 202–206 (2011)
Rojas, R.: Neural Networks: A Systematic Introduction, pp. 431–450. Springer, Berlin (1996)
Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by error propagation. In: Parallel Distributed Processing: Explorations in the Microstructure of Cognition, vol. 1, pp. 318–362. MIT Press, Cambridge (1986)
Takagi, T., Sugeno, M.: Derivation of fuzzy control rules from human operation control actions. In: Proceedings of the IFAC Symposium on Fuzzy Information, Knowledge Representation and Decision Analysis, pp. 55–60 (1983)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybernet. 15, 116–132 (1985)
Thomas, G.D.: Machine learning research: four current directions. Artif. Intell. Mag. 18(4), 97–136 (1997)
Wang, C., Zhang, J.P.: Time series prediction based on ensemble ANFIS. In: Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18–21 Aug 2005
Werbos, P.: Beyond regression: new tools for prediction and analysis in the behavioral sciences. PhD thesis, Harvard University (1974)
Xiaoyu, L., Bing, W., Simon, Y.: Time series prediction based on fuzzy principles. In: Department of Electrical & Computer Engineering FAMU-FSU College of Engineering. Florida State University Tallahassee, FL 32310 (2002)
Yager, R., Filev, D.: Essentials of Fuzzy Modeling and Control, p. 388. Wiley, New York (1994)
Zadeh, L.A.: Fuzzy Logic. Computer 1(4), 83–93 (1988)
Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 4(2), 103 (1996)
Zhou, Z.H., Wu, J., Tang, W.: Ensembling neural networks: many could be better than all. Artif. Intell. 137(1–2), 239–263 (2002)
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Soto, J., Melin, P. (2014). Genetic Optimization of Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction. In: Castillo, O., Melin, P., Pedrycz, W., Kacprzyk, J. (eds) Recent Advances on Hybrid Approaches for Designing Intelligent Systems. Studies in Computational Intelligence, vol 547. Springer, Cham. https://doi.org/10.1007/978-3-319-05170-3_6
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