Kalhor, A., Araabi, B., Lucasi, C. (2010). A New High-order Takagi-Sugeno Fuzzy Model Based on Deformed Linear Models. AUT Journal of Modeling and Simulation, 42(2), 43-54. doi: 10.22060/miscj.2010.210

Ahmad Kalhor; Babak N. Araabi; Caro Lucasi. "A New High-order Takagi-Sugeno Fuzzy Model Based on Deformed Linear Models". AUT Journal of Modeling and Simulation, 42, 2, 2010, 43-54. doi: 10.22060/miscj.2010.210

Kalhor, A., Araabi, B., Lucasi, C. (2010). 'A New High-order Takagi-Sugeno Fuzzy Model Based on Deformed Linear Models', AUT Journal of Modeling and Simulation, 42(2), pp. 43-54. doi: 10.22060/miscj.2010.210

Kalhor, A., Araabi, B., Lucasi, C. A New High-order Takagi-Sugeno Fuzzy Model Based on Deformed Linear Models. AUT Journal of Modeling and Simulation, 2010; 42(2): 43-54. doi: 10.22060/miscj.2010.210

A New High-order Takagi-Sugeno Fuzzy Model Based on Deformed Linear Models

Amongst possible choices for identifying complicated processes for prediction, simulation, and approximation applications, high-order Takagi-Sugeno (TS) fuzzy models are fitting tools. Although they can construct models with rather high complexity, they are not as interpretable as first-order TS fuzzy models. In this paper, we first propose to use Deformed Linear Models (DLMs) in consequence parts of a TS fuzzy model, which provides both complexity and interpretability. We then prove that in order to minimize considered error indices, linear and nonlinear parts of DLMs can be optimized independently. A localization of DLMs in input-space of the TS fuzzy model is done using an appropriate sigmoid-based membership function, which can represent a fuzzy subspace with enough smoothness and flat top. An incremental algorithm is also proposed to identify the suggested fuzzy model. Then, through an illustrative example, the formation of DLMs to approximate a nonlinear function is demonstrated. The applicability and effectiveness of the introduced fuzzy modeling approach is examined in three case studies: prediction of a chaotic time series, identification of a steam generator model, and approximation of a nonlinear function for a sun sensor. The obtained results demonstrate the higher accuracy and better generalization of our modeling approach as compared with those of some other well-known state-of-the-art approaches.

[1] T. Takagi, and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man Cybern., vol. 15, pp. 116-132, 1985.

[2] R. Jang, "ANFIS: Adaptive network-based fuzzy inference system," IEEE Trans. Syst., Man, Cybern., vol. 23, pp. 665-685, 1993.

[3] N. Kasabov, "DENFIS: Dynamic Evolving Neural-Fuzzy Inference System and its application for time-series prediction," IEEE Trans. Fuzzy Syst., vol. 10, pp. 144-154, 2002.

[4] Y. Chen, B. Yang, A. Abraham, and L. Peng, "Automatic design of hierarchical Takagi–Sugeno type fuzzy systems using evolutionary algorithms," IEEE Trans. Fuzzy Syst., vol. 15, pp. 385-397, 2007.

[5] J. Abonyi, R. Babuska, and F. Szeifert, "Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models," IEEE Trans. Syst. Man and Cybern.—PART B, vol. 32, pp. 612-621, 2002.

[6] P. Pulkkinen, and H. Koivisto, "Identification of interpretable and accurate fuzzy classifiersand function estimators with hybrid methods," Applied Soft Computing, vol. 7, pp. 520-533, 2007.

[7] C. F. Juang, "A self-organizing TS-type fuzzy network with support vector learning and its application to classification problems," IEEE Trans. Fuzzy Syst., vol. 15, pp. 998-1008, 2007.

[8] A. Kalhor, B. N. Araabi, and C. Lucas, "Online identification of a neuro-fuzzy model through indirect fuzzy clustering of data space," FUZZ-IEEE2009, the 18th Int. conference on fuzzy systems, 21-24 Aug., Korea, 2009, pp. 356-359.

[9] C. Li, J. Zhou, X. Xiang, Q. Li and X. An, "T–S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm," Engineering Applications of Artificial Intelligence, vol. 22, pp. 646–653, 2009.

[10] C .F. Juang, "A TSK-Type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms," IEEE Trans. Fuzzy Syst., vol. 10, pp. 155-170, 2008.

[11] H. Du, and N. Zhang, "Application of evolving Takagi–Sugeno fuzzy model to nonlinear system identification," Applied soft computing, vol. 8, pp. 876-686, 2007.

[12] L. Zhaoa , F. Qiana, Y. Yangb, Y. Zengb, and H. Sub, "Automatically extracting T–S fuzzy models using cooperative random learning particle swarm optimization," Applied Soft Computing , vol. 10, pp. 938-944, 2010.

[13] P.A. Mastorocostas, and J.B. Theocharis, "A recurrent fuzzy-neural model for dynamic system identification," IEEE Trans. Syst. Man Cybern., vol. 32, pp. 176-190, 2002.

[14] C. Li, and K. H. Cheng, " Recurrent neuro-fuzzy hybrid-learning approach to accurate system modelin," Fuzzy Sets and Systems, vol. 58, pp. 194-122, 2007.

[15] A. Savran, "An adaptive recurrent fuzzy system for nonlinear identification," Applied Soft Computing,vol. 7, pp. 593-600, 2007.

[16] O. Nelles, Nonlinear System Identification, New York: Springer, 2001, p. 365.

[17] A. Kalhor, B.N. Araabi, and C. Lucas, "A New Split and Merge Algorithm for Structure Identification in Takagi-Sugeno Fuzzy Model," in Proc. of 7th Int. Conf. on Intelligent Systems Design and Applications, 2007, pp. 258-261.

[18] A. Kalhor, B.N. Araabi, and C. Lucas, "An Online Predictor Model as Adaptive Habitually Linear and Transiently Nonlinear Model," Evolving Systems, vol. 1, pp. 29-41, 2010.

[19] B. Rezaee, and M.H.F. Zarandi, "Data-driven fuzzy modeling for Takagi–Sugeno–Kang fuzzy system," Information Sciences, vol. 180, pp. 241-255, 2010.

[20] J.B. Theocharis, "A high-order recurrent neuro-fuzzy system with internal dynamics: Application to the adaptive noise cancellation," Fuzzy Sets and Systems, vol. 157, pp. 471-500, 2006.

[21] Z.L. Sun, K. F. Au, and T. M. Choi, "A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines," IEEE Trans. Syst. Man Cybern.—PART B, vol. 37, pp. 1321-1331, 2007.

[22] J. N. Choi, S. K. Oh and W. Pedrycz, "Identification of fuzzy models using a successive tuning method with a variant identification ratio," Fuzzy Sets and Systems, vol. 159, pp. 2873-2889, 2008.

[23] K. B. Petersen, and M. S. Pedersen, "The matrix cookbook," Available: http://matrixcookbook.com, Version: Nov. 14, 2008.

[24] De Moor B.L.R. (ed.) , "DaISy: Database for the Identification of Systems," Department of Electrical Engineering, ESAT/SISTA, K.U.Leuven, Belgium, Available: http://www.esat.kuleuven.ac.be/sista/daisy.