The Transactions of The Korean Institute of Electrical Engineers (전기학회논문지)

The Korean Institute of Electrical Engineers (대한전기학회)
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Structural Design of FCM-based Fuzzy Inference System : A Comparative Study of WLSE and LSE

FCM기반 퍼지추론 시스템의 구조 설계: WLSE 및 LSE의 비교 연구

  • Received : 2009.12.09
  • Accepted : 2010.02.10
  • Published : 2010.05.01
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Abstract

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.

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References

  1. L.A Zadeh " Fuzzy sets," Inf. contol 8, pp.338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
  2. Mahmut Firat, Mustafa Erkan Turan, Mehmet Ali Yurdesev, "Comparative analysis of fuzzy inference systems for water consumption time series prediction," Journal of Hydrology, Vol.374, No.3-4, pp.235-241, 2009.
  3. Aboozar Khajeh, Hamid Modarress, Babak Rezzaee, "Appplication of adaptive neuro-fuzzy inference system for solubility prediction of carbon dioxide in polymers," Expert systems with Application, Vol.36, No.3, pp.5728-5732, 2009 https://doi.org/10.1016/j.eswa.2008.06.051
  4. Cheng-jian Lin, "An efficient immune-based symbiotic particle swarm optimization learning algorithm for TSK-type neuro-fuzzy networks design," Fuzzy ets and Systems, Vol.159, No.21, pp.2890-2909, 2008. https://doi.org/10.1016/j.fss.2008.01.020
  5. Cheng-Jian Lin, Shang-Jin Hong "The design of neuro-fuzzy networks using particle swarm optimization and recursive singular value decomposition", Neurocomputing, Vol.71, No.1-3, pp.297-310, 2009.
  6. A. Staiano. j. Tagliaferri, W. Pedrycz, "Improving RBF networks performance in regression tasks by means of a supervised fuzzy clustering Automatic structure and parameter," Neurocomputing, Vol.69, pp.1570-1581, 2006. https://doi.org/10.1016/j.neucom.2005.06.014
  7. Qiuming Zhu, Yao Luzheng Liu, "A global learning algorithm for a RBF network," Neural Networks, Vol.12, No.3, pp.527-540, 1999. https://doi.org/10.1016/S0893-6080(98)00146-4
  8. Ho-Sung Park, Witold Pedrycz, Sung-Kwun Oh, "Evolutionary design of hybrid self-organizing fuzzy polynomial neural networks with the aid of information granulation," Expert systems with Applications, Vol.33, No.4, pp.830-846, 2007. https://doi.org/10.1016/j.eswa.2006.07.006
  9. S. Abbasbandy, M. Otadi, M. Mosleh, "Numerical solution of a system of fuzzy polynomial by fuzzy neural network," Information Sciences, Vol.178, No.8, pp.1948-1960, 2008. https://doi.org/10.1016/j.ins.2007.11.026
  10. Sung-Kwun Oh, Witold Pedrycz, Seok-Beom Roh, "Hybrid fuzzy set-based polynomial neural networks and their development with the aid of genetic optimization and information granulation," Applied Soft Computing, Vol.9, No.3, pp.1068-1089, 2009. https://doi.org/10.1016/j.asoc.2009.02.007
  11. Jeoung-Nae Choi, Sung-Kwun Oh, Witold Pedrycz," Identification of fuzzy relation models using hierarchical fair competition-based parallel genetic algorithms and information granulation," Applied mathematical Modeling, Vol.33, No.6 pp.2791-2807, 2009. https://doi.org/10.1016/j.apm.2008.08.022
  12. W. Pedrycz. K.C. Kwak, "Linguistic models as a framework of user-centric system modeling," IEEE, Trans. Syst. Man Cybern. A, Vol.36, No.4, pp.727-745, 2006. https://doi.org/10.1109/TSMCA.2005.855755
  13. J.S. Roger Jang, "ANFIS: Adaptive-Network-based Fuzzy Inference System," IEEE, Trans. Syst. Man, Sybern, Vol.23, No.3, pp.665-685, 1993. https://doi.org/10.1109/21.256541
  14. Sung-Kwun Oh, withold Pedrycz, Seok-Beom Roh, "Hybrid fuzzy set-based polynomial neural networks and their development with the aid of genetic optimization and information granulation," Applied soft computing, Vol.9, No.3, pp.1068-1089, 2009. https://doi.org/10.1016/j.asoc.2009.02.007