A novel function approximation based on robust fuzzy regression algorithm model and particle swarm optimization

In this paper, a novel approach for function approximation based on robust fuzzy regression algorithm and particle swarm optimization is proposed. First, the robust fuzzy regression algorithm is applied to construct Takagi-Sugeno-Kang fuzzy model. The robust fuzzy regression algorithm is not only to simultaneously identify parameters in the premise parts and the consequent parts, but it also defines the number of fuzzy rules to fit for Takagi-Sugeno-Kang model. In addition, the robust fuzzy regression algorithm has robust learning effects when noise and outliers exist. Thereafter, particle swarm optimization is conducted to fine tune parameters from obtained fuzzy model. In simulation results, particle swarm optimization can improve Takagi-Sugeno-Kang fuzzy model built by robust fuzzy regression algorithm efficiently. The proposed approach can find best solutions when compared with other learning algorithms for four test functions.

[1]  Ke Zeng,et al.  A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators , 2000, IEEE Trans. Fuzzy Syst..

[2]  Ludmila I. Kuncheva,et al.  Fuzzy Classifier Design , 2000, Studies in Fuzziness and Soft Computing.

[3]  R.J. Hathaway,et al.  Switching regression models and fuzzy clustering , 1993, IEEE Trans. Fuzzy Syst..

[4]  Jian Yu,et al.  Alpha-Cut Implemented Fuzzy Clustering Algorithms and Switching Regressions , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Chia-Feng Juang,et al.  Temperature control by chip-implemented adaptive recurrent fuzzy controller designed by evolutionary algorithm , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[6]  Ramesh C. Jain,et al.  A robust backpropagation learning algorithm for function approximation , 1994, IEEE Trans. Neural Networks.

[7]  Xiao-Jun Zeng,et al.  Approximation theory of fuzzy systems-SISO case , 1994, IEEE Trans. Fuzzy Syst..

[8]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[9]  V. J. Rayward-Smith,et al.  Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition , 1999 .

[10]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[11]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Hichem Frigui,et al.  A Robust Competitive Clustering Algorithm With Applications in Computer Vision , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Shigeo Abe.  Fuzzy function approximators with ellipsoidal regions , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Jerry M. Mendel,et al.  Generating fuzzy rules by learning from examples , 1992, IEEE Trans. Syst. Man Cybern..

[15]  Shun-Feng Su,et al.  The annealing robust backpropagation (ARBP) learning algorithm , 2000, IEEE Trans. Neural Networks Learn. Syst..

[16]  Zne-Jung Lee,et al.  A robust learning algorithm based on support vector regression and robust fuzzy cerebellar model articulation controller , 2008, Applied Intelligence.

[17]  Zne-Jung Lee.  A novel hybrid algorithm for function approximation , 2008, Expert Syst. Appl..

[18]  Rajesh N. Davé,et al.  Robust clustering methods: a unified view , 1997, IEEE Trans. Fuzzy Syst..

[19]  Peter J. Angeline,et al.  Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences , 1998, Evolutionary Programming.

[20]  Shigeo Abe,et al.  Neural Networks and Fuzzy Systems: Theory and Applications , 2012 .

[21]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[22]  Shigeo Abe,et al.  Function approximation based on fuzzy rules extracted from partitioned numerical data , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[23]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[24]  Hao Ying,et al.  Sufficient conditions on general fuzzy systems as function approximators , 1994, Autom..

[25]  Zhihong Man,et al.  A New Adaptive Backpropagation Algorithm Based on Lyapunov Stability Theory for Neural Networks , 2006, IEEE Transactions on Neural Networks.

[26]  Zne-Jung Lee,et al.  A genetic algorithm based robust learning credit assignment cerebellar model articulation controller , 2004, Appl. Soft Comput..

[27]  Chen-Chia Chuang,et al.  A novel approach for TSK fuzzy modeling with outliers , 2003, Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693).

[28]  Hsuan-Ming Feng,et al.  Particle swarm optimization learning fuzzy systems design , 2005, Third International Conference on Information Technology and Applications (ICITA'05).

[29]  Wan-Jun Hao,et al.  Fuzzy Controller Design and Parameter Optimization , 2006, 2006 International Conference on Machine Learning and Cybernetics.

[30]  Song-Shyong Chen,et al.  Robust TSK fuzzy modeling for function approximation with outliers , 2001, IEEE Trans. Fuzzy Syst..

[31]  Riccardo Rovatti,et al.  Fuzzy piecewise multilinear and piecewise linear systems as universal approximators in Sobolev norms , 1998, IEEE Trans. Fuzzy Syst..

[32]  Lei Wang,et al.  Fuzzy logic based multi-optimum programming in particle swarm optimization , 2005, Proceedings. 2005 IEEE Networking, Sensing and Control, 2005..

[33]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[34]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[35]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[36]  Uzay Kaymak,et al.  Fuzzy Decision Making in Modeling and Control , 2002, World Scientific Series in Robotics and Intelligent Systems.