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2014 | OriginalPaper | Buchkapitel

Genetic Optimization of Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction

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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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Literatur
1.
Zurück zum Zitat Brocklebank, J.C., Dickey, D.A.: SAS for Forecasting Series, pp. 6–140. SAS Institute Inc, Cary (2003)MATH Brocklebank, J.C., Dickey, D.A.: SAS for Forecasting Series, pp. 6–140. SAS Institute Inc, Cary (2003)MATH
2.
Zurück zum Zitat Brockwell, P.D., Richard, A.D.: Introduction to Time Series and Forecasting, pp. 1–219. Springer, New York (2002)MATH Brockwell, P.D., Richard, A.D.: Introduction to Time Series and Forecasting, pp. 1–219. Springer, New York (2002)MATH
3.
Zurück zum Zitat 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)CrossRef 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)CrossRef
4.
Zurück zum Zitat Castillo, O., Melin, P.: Soft Computing for Control of Non-Linear Dynamical Systems. Springer, Heidelberg (2001)CrossRefMATH Castillo, O., Melin, P.: Soft Computing for Control of Non-Linear Dynamical Systems. Springer, Heidelberg (2001)CrossRefMATH
5.
Zurück zum Zitat 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., Martínez, L.G.: Interval type-2 fuzzy logic toolbox. Eng. Lett. 15(1), 89–98 (2007)
6.
Zurück zum Zitat 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., 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)
7.
Zurück zum Zitat 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) 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)
8.
Zurück zum Zitat 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) 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)
9.
Zurück zum Zitat 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)CrossRefMATHMathSciNet 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)CrossRefMATHMathSciNet
10.
Zurück zum Zitat Cordon, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy, Knowledge Bases. World Scientific, Singapore (2001)CrossRef Cordon, O., Herrera, F., Hoffmann, F., Magdalena, L.: Genetic Fuzzy Systems: Evolutionary Tuning and Learning of Fuzzy, Knowledge Bases. World Scientific, Singapore (2001)CrossRef
11.
Zurück zum Zitat 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)CrossRefMATH 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)CrossRefMATH
12.
Zurück zum Zitat 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)MathSciNet 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)MathSciNet
13.
Zurück zum Zitat Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computation, pp. 37–69. Springer, Berlin (2003) Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computation, pp. 37–69. Springer, Berlin (2003)
14.
Zurück zum Zitat Filev, D., Yager, R.: On the issue of obtaining OWA operador weights. Fuzzy Sets Syst. 94(2), 157–169 (1998)CrossRefMathSciNet Filev, D., Yager, R.: On the issue of obtaining OWA operador weights. Fuzzy Sets Syst. 94(2), 157–169 (1998)CrossRefMathSciNet
15.
Zurück zum Zitat 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., 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)
16.
Zurück zum Zitat Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Boston (1989)MATH Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Boston (1989)MATH
17.
Zurück zum Zitat Goldberg, D.E., Korb, B., Kalyanmoy, D.: Messy genetic algorithms: motivation, analysis, and first results. Complex Syst. 3, 493–530 (1989)MATH Goldberg, D.E., Korb, B., Kalyanmoy, D.: Messy genetic algorithms: motivation, analysis, and first results. Complex Syst. 3, 493–530 (1989)MATH
18.
Zurück zum Zitat Holland, J.H.: Outline for a logical theory of adaptive systems. J. Assoc. Comput. Mach. 3, 297–314 (1962)CrossRef Holland, J.H.: Outline for a logical theory of adaptive systems. J. Assoc. Comput. Mach. 3, 297–314 (1962)CrossRef
19.
Zurück zum Zitat Holland, J.H.: Adaptatioon in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975) Holland, J.H.: Adaptatioon in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
20.
Zurück zum Zitat Jang, J.S.R.: ANFIS: adaptive-network-based fuzzy inference systems. IEEE Trans. Syst. Man Cybernet. 23, 665–685 (1992)CrossRef Jang, J.S.R.: ANFIS: adaptive-network-based fuzzy inference systems. IEEE Trans. Syst. Man Cybernet. 23, 665–685 (1992)CrossRef
21.
Zurück zum Zitat 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.: 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)
22.
Zurück zum Zitat Jang, J.S.R.: Rule extraction using generalized neural networks. In: Proceedings of the 4th IFSA Wolrd Congress, pp. 82–86 (1991) Jang, J.S.R.: Rule extraction using generalized neural networks. In: Proceedings of the 4th IFSA Wolrd Congress, pp. 82–86 (1991)
23.
Zurück zum Zitat Konar, A.: Computational Intelligence: Principles, Techniques and Applications. Springer, Berlin (2005)CrossRef Konar, A.: Computational Intelligence: Principles, Techniques and Applications. Springer, Berlin (2005)CrossRef
24.
Zurück zum Zitat Lawrence, D.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New Jersey (1991) Lawrence, D.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New Jersey (1991)
25.
Zurück zum Zitat Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287–289 (1997)CrossRef Mackey, M.C., Glass, L.: Oscillation and chaos in physiological control systems. Science 197, 287–289 (1997)CrossRef
27.
Zurück zum Zitat 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)CrossRef 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)CrossRef
28.
Zurück zum Zitat 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 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
29.
Zurück zum Zitat 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.: Why we need type-2 fuzzy logic systems (Article is provided courtesy of Prentice Hall, By Jerry Mendel) 11 May 2001
30.
Zurück zum Zitat Mendel, J.M. (ed.): Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, pp. 25–200. Prentice Hall, USA (2000) Mendel, J.M. (ed.): Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, pp. 25–200. Prentice Hall, USA (2000)
31.
Zurück zum Zitat Mendel, J.M., Mouzouris, G.C.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7, 643–658 (1999)CrossRef Mendel, J.M., Mouzouris, G.C.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7, 643–658 (1999)CrossRef
32.
Zurück zum Zitat Michalewicz, Z.: Genetic Algorithms + Data Structures=Evolution Programs, vol. AI. Springer-Verlag, New York (1994)CrossRefMATH Michalewicz, Z.: Genetic Algorithms + Data Structures=Evolution Programs, vol. AI. Springer-Verlag, New York (1994)CrossRefMATH
33.
Zurück zum Zitat 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) 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)
34.
Zurück zum Zitat Rojas, R.: Neural Networks: A Systematic Introduction, pp. 431–450. Springer, Berlin (1996)CrossRef Rojas, R.: Neural Networks: A Systematic Introduction, pp. 431–450. Springer, Berlin (1996)CrossRef
35.
Zurück zum Zitat 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) 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)
36.
Zurück zum Zitat 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.: 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)
37.
Zurück zum Zitat Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybernet. 15, 116–132 (1985)CrossRefMATH Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybernet. 15, 116–132 (1985)CrossRefMATH
38.
Zurück zum Zitat Thomas, G.D.: Machine learning research: four current directions. Artif. Intell. Mag. 18(4), 97–136 (1997) Thomas, G.D.: Machine learning research: four current directions. Artif. Intell. Mag. 18(4), 97–136 (1997)
39.
Zurück zum Zitat 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 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
40.
Zurück zum Zitat Werbos, P.: Beyond regression: new tools for prediction and analysis in the behavioral sciences. PhD thesis, Harvard University (1974) Werbos, P.: Beyond regression: new tools for prediction and analysis in the behavioral sciences. PhD thesis, Harvard University (1974)
41.
Zurück zum Zitat 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) 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)
42.
Zurück zum Zitat Yager, R., Filev, D.: Essentials of Fuzzy Modeling and Control, p. 388. Wiley, New York (1994) Yager, R., Filev, D.: Essentials of Fuzzy Modeling and Control, p. 388. Wiley, New York (1994)
45.
Zurück zum Zitat Zhou, Z.H., Wu, J., Tang, W.: Ensembling neural networks: many could be better than all. Artif. Intell. 137(1–2), 239–263 (2002)CrossRefMATHMathSciNet Zhou, Z.H., Wu, J., Tang, W.: Ensembling neural networks: many could be better than all. Artif. Intell. 137(1–2), 239–263 (2002)CrossRefMATHMathSciNet
Metadaten
Titel
Genetic Optimization of Type-2 Fuzzy Integrators in Ensembles of ANFIS Models for Time Series Prediction
verfasst von
Jesus Soto
Patricia Melin
Copyright-Jahr
2014
DOI
https://doi.org/10.1007/978-3-319-05170-3_6