A novel hybrid algorithm for function approximation

This paper introduces a novel hybrid algorithm for function approximation. The proposed algorithm consists of a hybrid approach to develop Takagi and Sugeno's fuzzy model for function approximation. In this paper, a coarse tuning based on Takagi and Sugeno's fuzzy model is applied to identify the fuzzy structure, and also a fuzzy cluster validity index is utilized to determine the optimal number of clusters. To obtain a more precision model, genetic algorithm (GA) and particle swarm optimization (PSO) are performed to conduct fine-tuning for the obtained parameter set of the premise parts and consequent parts in the aforementioned fuzzy model. The proposed algorithm is successfully applied to three tested examples. Compared with other existing approaches in the literature, the proposed algorithm is very useful for modeling function approximation.

[1]  Chin-Teng Lin,et al.  An online self-constructing neural fuzzy inference network and its applications , 1998, IEEE Trans. Fuzzy Syst..

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

[3]  Haralambos Sarimveis,et al.  A hierarchical fuzzy-clustering approach to fuzzy modeling , 2005, Fuzzy Sets Syst..

[4]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

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

[6]  Euntai Kim,et al.  A transformed input-domain approach to fuzzy modeling , 1998, IEEE Trans. Fuzzy Syst..

[7]  Euntai Kim,et al.  A new approach to fuzzy modeling , 1997, IEEE Trans. Fuzzy Syst..

[8]  Chuen-Tsai Sun,et al.  Neuro-fuzzy And Soft Computing: A Computational Approach To Learning And Machine Intelligence [Books in Brief] , 1997, IEEE Transactions on Neural Networks.

[9]  H Tanaka,et al.  A SIMPLE BUT POWERFUL METHOD FOR GENERATING FUZZY RULES FROM NUMERICAL DATA , 1997 .

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

[11]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[12]  Andreas Kroll,et al.  Identification of functional fuzzy models using multidimensional reference fuzzy sets , 1996, Fuzzy Sets Syst..

[13]  C. S. George Lee,et al.  Neural fuzzy systems: a neuro-fuzzy synergism to intelligent systems , 1996 .

[14]  Ujjwal Maulik,et al.  A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification , 2005, Fuzzy Sets Syst..

[15]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[16]  Hisao Ishibuchi,et al.  A simple but powerful heuristic method for generating fuzzy rules from numerical data , 1997, Fuzzy Sets Syst..

[17]  Frank Klawonn,et al.  Constructing a fuzzy controller from data , 1997, Fuzzy Sets Syst..

[18]  Abdulkadir Sengur,et al.  Comparison of clustering algorithms for analog modulation classification , 2006 .

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

[20]  Ronald R. Yager,et al.  Essentials of fuzzy modeling and control , 1994 .

[21]  Antonio F. Gómez-Skarmeta,et al.  About the use of fuzzy clustering techniques for fuzzy model identification , 1999, Fuzzy Sets Syst..

[22]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[23]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

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

[25]  Bart Kosko,et al.  Fuzzy function approximation with ellipsoidal rules , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[26]  Chao-Ming Huang,et al.  A particle swarm optimization to identifying the ARMAX model for short-term load forecasting , 2005 .

[27]  Chou-Yuan Lee,et al.  Efficiently solving general weapon-target assignment problem by genetic algorithms with greedy eugenics , 2003, IEEE Trans. Syst. Man Cybern. Part B.

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