# A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

Moêz Soltani; Abdelkader Chaari; Fayçal Ben Hmida

International Journal of Applied Mathematics and Computer Science (2012)

- Volume: 22, Issue: 3, page 617-628
- ISSN: 1641-876X

## Access Full Article

top## Abstract

top## How to cite

topMoêz Soltani, Abdelkader Chaari, and Fayçal Ben Hmida. "A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization." International Journal of Applied Mathematics and Computer Science 22.3 (2012): 617-628. <http://eudml.org/doc/244058>.

@article{MoêzSoltani2012,

abstract = {This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.},

author = {Moêz Soltani, Abdelkader Chaari, Fayçal Ben Hmida},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {Takagi-Sugeno fuzzy model; noise clustering algorithm; fuzzy c-regression model; orthogonal least squares; particle swarm optimization},

language = {eng},

number = {3},

pages = {617-628},

title = {A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization},

url = {http://eudml.org/doc/244058},

volume = {22},

year = {2012},

}

TY - JOUR

AU - Moêz Soltani

AU - Abdelkader Chaari

AU - Fayçal Ben Hmida

TI - A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

JO - International Journal of Applied Mathematics and Computer Science

PY - 2012

VL - 22

IS - 3

SP - 617

EP - 628

AB - This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.

LA - eng

KW - Takagi-Sugeno fuzzy model; noise clustering algorithm; fuzzy c-regression model; orthogonal least squares; particle swarm optimization

UR - http://eudml.org/doc/244058

ER -

## References

top- Alci, M. (2008). Fuzzy rule-base driven orthogonal approximation, Neural Computing and Applications 17(5-6): 501-507.
- Andri, R. and Ennu, R. (2011). Identification of transparent, compact, accurate and reliable linguistic fuzzy models, Information Sciences 181(20): 4378-4393.
- Ben, N., Yunlong, Z., Xiaoxian, H. and Hai, S. (2008). A multi-swarm optimizer based fuzzy modeling approach for dynamic systems processing, Neurocomputing 71(7-9): 1436-1448.
- Bezdek, J.C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, NY. Zbl0503.68069
- Bezdek, J.C., Keller, J., Krisnapuram, R. and Pal, N. (1999). Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, Vol. 4, Springer, New York, NY. Zbl0998.68138
- Bidyadhar, S. and Debashisha, J. (2011). A differential evolution based neural network approach to nonlinear identification, Applied Soft Computing 11(1): 861-871.
- Boukhris, A., Mourot, G. and Ragot, J. (1999). Nonlinear invisible system identification: A multi-model approach, International Journal of Control 72(7-8): 591-604. Zbl0938.93512
- Box, G.E.P. and Jenkins, G.M. (1970). Times Series Analysis, Holden Day, San Francisco, CA. Zbl0249.62009
- Brdyś, A.M. and Littler, J.J. (2002). Fuzzy logic gain scheduling for non-linear servo tracking, International Journal of Applied Mathematics and Computer Science 12(2): 209-219. Zbl1004.93502
- Celikyilmaz, A. and Burhan Turksen, I. (2008). Enhanced fuzzy system models with improved fuzzy clustering algorithm, IEEE Transactions on Fuzzy Systems 16(3): 779-794.
- Chaoshun, L., Jianzhong, Z., Xiuqiao, X., Qingqing, L. and Xueli, A. (2010). A new T-S fuzzy-modeling identification approach to identify a boiler-turbine, Expert Systems with Applications 37(3): 2214-2221.
- Chaoshun, L., Jianzhong, Z., Xiuqiao, X., Qingqing, L. and Xueli, A. (2009). T-S fuzzy model identification based on a novel fuzzy c-regression model clustering algorithm, Engineering Applications of Artificial Intelligence 22 (4-5): 646-653.
- Chen, J.L. and Wang, J.H. (1999). A new robust clustering algorithm-density-weighted fuzzy c-means, Proceedings of the IEEE Conference on Systems, Man, and Cybernetics, SMC 1999, Tokyo, Japan, pp. 12-15.
- Chen, J.Q., Xi, Y.G. and Zhang, Z.J. (1998). A clustering algorithm for fuzzy model identification, International Journal of Control 98(3): 319-329.
- Chen, S., Billings, S.A. and Luo, W. (1989). Orthogonal least squares methods and their application to nonlinear system identification, International Journal of Control 50(5): 1873-1896. Zbl0686.93093
- Dave, R.N. (1991). Characterization and detection of noise in clustering, Pattern Recognition Letters 12(11): 657-664.
- Dave, R.N. and Krishnapuram, R. (1997). Robust clustering methods: A unified view, IEEE Transactions on Fuzzy Systems 5(2): 270-293.
- Frigui, H. and Krishnapuram, R. (1999). A robust competitive clustering algorithm with applications in computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence 21(5): 450-465.
- Gath, I. and Geva, A. (1989). Unsupervised optimal fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7): 773-780. Zbl0709.62592
- Gustafson, D.E. and Kessel, W.C. (1979). Fuzzy clustering with a fuzzy covariance matrix, Proceedings of the IEEE Conference on Decision Control, CDC 1978, San Diego, CA, USA, pp. 761-766.
- Hathaway, R.J. and Bezdek, J.C. (1993). Switching regression models and fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 1(3): 195-204.
- Hellendoorn, H. and Driankov, D. (1997). Fuzzy Model Identification: Selected Approaches, Springer, Berlin. Zbl0874.00030
- Honda, K., Notsu, A. and Ichihashi, H. (2010). Fuzzy PCAguided robust k-means clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 18(1): 67-79.
- Hoppner, F., Klawonn, F., Kruse, R. and Runkler, T. (1999). Fuzzy Cluster Analysis, Methods for Classification, Data Analysis and Image Recognition, 1st Edn., John Wiley and Sons, Chichester. Zbl0944.65009
- Ichalal, D., Marx, B., Ragot, J. and Maquin, D. (2010). Observer based fault tolerant control for nonlinear Takagi-Sugeno systems: An LMI approach, Proceedings of the 18th Mediterranean Conference on Control and Automation, MED 2010, Marrakech, Marocco, pp. 1278-1283. Zbl1273.93102
- Ichihashi, H. and Honda, K. (2004). On parameter setting in applying Dave's noise fuzzy clustering to Gaussian mixture models, Proceedings of the 13th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2004, Budapest, Hungary, pp. 1501-1506.
- Ichihashi, H., Honda, K. and Wakami, N. (2005). Robust PCA with intra-sample outlier process based on fuzzy Mahalanobis distances and noise clustering, Proceedings of the 14th IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2005, Reno, NV, USA, pp. 640-645.
- Kennedy, J. and Eberhart, R. C. (1995). Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks, ICNN 1995, Perth, Australia, pp. 1942-1948.
- Kim, E., Park, M., Kim, S. and Park, M. (1998). A transformed input-domain approach to fuzzy modeling, IEEE Transactions on Fuzzy Systems 6(4): 596-604.
- Kim, K., Kim, Y.K., Kim, E. and Park, M. (2004). A new TSK fuzzy modeling approach, Proceedings of the IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2004, Budapest, Hungary, pp. 773-776.
- Kluska, J. (2009). Analytical Methods in Fuzzy Modeling and Control, Studies in Fuzziness and Soft Computing, Springer-Verlag, Berlin/Heidelberg. Zbl1226.93002
- Kościelny, J.M. and Syfert, M. (2006). Fuzzy diagnostic reasoning that takes into account the uncertainty of the relation between faults and symptoms, International Journal of Applied Mathematics and Computer Science 16(1): 27-35. Zbl1334.93104
- Leski, J.M. (2004). ϵ-insensitive fuzzy c-regression models: Introduction to ϵ-insensitive fuzzy modeling, IEEE Transactions on Systems, Man, and Cybernetics 34(1): 4-15.
- Liang, Z., Yang, Y. and Zeng, Y. (2009). Eliciting compact T-S fuzzy models using subtractive clustering and coevolutionary particle swarm optimization, Neurocomputing 72(10-12): 2569-2575.
- Marx, B., Koenig, D. and Ragot, J. (2007). Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis, IET Control Theory and Applications 1(5): 1487-1495.
- Nasraoui, O. and Krishnapuram, R. (1996). An improved possibilistic c-means algorithm with finite rejection and robust scale estimation, Biennial Conference of the North American Fuzzy Information Processing Society, NAFIPS 1996, Berkeley, CA, USA, pp. 395-399.
- Niknam, T. and Amiri, B. (2010). An efficient hybrid approach based on PSO, ACO and k-means for cluster analysis, Applied Soft Computing 10(1): 183-197.
- Ohashi, Y. (1984). Fuzzy clustering and robust estimation, 9th Meeting, SAS Users Group International, Hollywood Beach, FL, USA, pp. 1-6.
- Panchal, V.K., Harish, K. and Jagdeep, K. (2009). Comparative study of particle swarm optimization based unsupervised clustering techniques, International Journal of Computer Science and Network Security 9(10): 132-140.
- Qi, R. and Brdys, M.A. (2009). Indirect adaptive controller based on a self-structuring fuzzy system for nonlinear modeling and control, International Journal of Applied Mathematics and Computer Science 19(4): 619-630, DOI: 10.2478/v10006-009-0049-8. Zbl1300.93100
- Qiang, N. and Xinjian, H. (2011). An improved fuzzy c-means clustering algorithm based on PSO, Journal of Software 6(5): 873-879.
- Rezaee, B. and Zarandi, M.H.F. (2010). Data-driven fuzzy modeling for Takagi-Sugeno-Kang fuzzy system, Information Sciences 180(2): 241-255.
- Soltani, M., Aissaoui, B., Chaari, A., Ben Hmida, F. and Gossa, M. (2011). A modified fuzzy c-regression model clustering algorithm for T-S fuzzy model identification, Proceedings of the 8th IEEE International Multi-Conference on Systems, Signals and Devices, SSD 2011, Sousse, Tunisia, pp. 1-6.
- Soltani, M., Chaari, A., Ben Hmida, F. and Gossa, M. (2010a). Modified fuzzy model identification clustering algorithm for liquid level process, Proceedings of the 18th Mediterranean Conference on Control and Automation, MED 2010, Marrakech, Morocco, pp. 1151-1157.
- Soltani, M., Chaouchi, L., Chaari, A., Ben Hmida, F. and Moncef, G. (2010b). Identification of nonlinear complex systems using uncoupled state fuzzy model for liquid level process, International Review of Automatic Control 3(5): 535-544.
- Sumit, S. and Dave, R.N. (1998). Clustering of relational data containing noise and outliers, Proceedings of the 7th IEEE International Conference on Fuzzy Systems/World Congress on Computational Intelligence, Anchorage, AK, USA, Vol. 2, pp. 1411-1416.
- Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Transactions on Systems, Man, and Cybernetics 15(1): 116-132. Zbl0576.93021
- Tran, D. and Wagner, M. (1999). A robust clustering approach to fuzzy gaussian mixture models for speaker identification, Proceedings of the 3rd International Conference on Knowledge-Based Intelligent Information Engineering Systems, KES 1997, Adelaide, SA, Australia, pp. 337-340.
- Wang, L.X. and Mendel, J.M. (1992). Fuzzy basis functions, universal approximation, and orthogonal leastsquares learning, IEEE Transactions on Neural Networks 3(5): 807-814.
- Wu, K.L. and Yang, M.S. (2002). Alternative c-means clustering algorithms, Pattern Recognition 35(10): 2267-2278. Zbl1006.68876
- Wu, X.F., Lang, Z.Q. and Billings, S.A. (2005). An orthogonal least squares based approach to FIR designs, International Journal of Automation and Computing 2(2): 163-170.
- Xu, Y.F. and Zhang, S.L. (2009). Fuzzy particle swarm clustering of infrared images, Proceedings of the 2009 2nd International Conference on Information and Computing Science, ICIC 2009, Manchester, UK, Vol. 2, pp. 122-124.
- Yang, X., Song, Q. and Liu, S. (2005). Robust deterministic annealing algorithm for data clustering, Proceedings of the International Joint Conference on Neural Networks, IJCNN 2005, Montreal, Canada, pp. 1878-1882.
- Ying, H. (2000). Fuzzy Control and Modeling: Analytical Foundations and Applications, IEEE Press, New York, NY.
- Ying, K.C., Lin, S.W., Lee, Z.J. and Lee, I.L. (2011). A novel function approximation based on robust fuzzy regression algorithm model and particle swarm optimization, Applied Soft Computing 38(2): 1820-1826.
- Zhang, D., Liu, X. and Guan, Z. (2006). A dynamic clustering algorithm based on PSO and its application in fuzzy identification, Proceedings of the International Conference on Intelligent Information Hiding and Multimedia Signal Processing, IIH-MSP 2006, Pasadena, CA, USA, pp. 232-235.
- Zhang, Y., Huang, D., Ji, M. and Xie, F. (2011). Image segmentation using PSO and PCM with Mahalanobis distance, Expert Systems with Applications 38(7): 9036-9040.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.