Design of Hybrid Fuzzy Neural Network for Function Approximation

ABSTRACT

In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the Fuzzy rule based knowledge is translated directly into network architecture. The connections between input to hidden nodes represent rule antecedents and hidden to output nodes represent rule consequents. All the connections are represented by Gaussian fuzzy sets. The method of activation spread in the network is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric o fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has been tested on two different approximation problems: sine-cosine function approximation and Narazaki-Ralescu function and shows its natural capability of inference, function approximation, and classification.

In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the Fuzzy rule based knowledge is translated directly into network architecture. The connections between input to hidden nodes represent rule antecedents and hidden to output nodes represent rule consequents. All the connections are represented by Gaussian fuzzy sets. The method of activation spread in the network is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric o fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has been tested on two different approximation problems: sine-cosine function approximation and Narazaki-Ralescu function and shows its natural capability of inference, function approximation, and classification.

Cite this paper

nullA. Mishra and Z. Zaheeruddin, "Design of Hybrid Fuzzy Neural Network for Function Approximation,"*Journal of Intelligent Learning Systems and Applications*, Vol. 2 No. 2, 2010, pp. 97-109. doi: 10.4236/jilsa.2010.22013.

nullA. Mishra and Z. Zaheeruddin, "Design of Hybrid Fuzzy Neural Network for Function Approximation,"

References

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[11] R.-J. Wai and Z.-W. Yang, “Adaptive Fuzzy Neural Network Control Design via a T-S Fuzzy Model for a Robot Manipulator Including Actuator Dynamics,” IEEE Transactions on System, Man and Cybernetics-Part B, Vol. 38, No. 5, 2008, pp. 1326-1346.

[12] P. Sandeep and S. Kumar, “Subsethood Based Adaptive Linguistic Networks for Pattern Classification,” IEEE Transaction on System, man and cybernetics-part C: application and reviews, Vol. 33, No. 2, 2003, pp. 248-258.

[13] B. Kosko, “Fuzzy Engineering,” Prentice-Hall, Englewood Cliffs, New Jersey, 1997.

[14] K. Hornik, “Approximation Capabilities of Multilayer Feed forward Networks are Universal Approximators,” IEEE Transaction on Neural Networks, Vol. 2, No. 5, 1989, pp. 359-366.

[15] B. Kosko, “Fuzzy Systems as Universal Approximators,” IEEE Transactions on computers, Vol. 43, No. 11, 1994, pp. 1329-1333.

[16] C. T. Lin and Y. C. Lu, “A Neural Fuzzy System with Linguistic Teaching Signals,” IEEE Transactions Fuzzy Systems, Vol. 3, No. 2, 1995, pp. 169-189.

[17] L. X. Wang and J. M. Mendel, “Generating Fuzzy Rules from Numerical Data, with Application,” Technical Report 169, USC SIPI, University of Southern California, Los Angeles, January 1991.

[18] H. Narazaki and A. L. Ralescu, “An Improved Synthesis Method for Multilayered Neural Networks Using Qualitative Knowledge’s,” IEEE Transactions Fuzzy Systems, Vol. 1, No. 2, 1993, pp. 125-137.

[19] M. Russo, “FuGeNeSys-a Fuzzy Genetic Neural System for Fuzzy Modeling,” IEEE Transactions Fuzzy Systems, Vol. 6, No. 3, 1993, pp. 373-388.

[20] Y. Lin and G. A. Cunningham, “A New Approach to Fuzzy-Neural System Modeling,” IEEE Transactions Fuzzy Systems, Vol. 3, No. 2, 1995, pp. 190-198.

[1] C. T. Lin and C. S. G. Lee, “Neural-Network-Based Fuzzy Logic Control and Decision System,” IEEE Transactions on Computers, Vol. 40, No. 12, 1991, pp. 1320-1336.

[2] J. M. Keller, R. R. Yager and H. Tahani, “Neural Network Implementation of Fuzzy Logic,” Fuzzy Sets and Systems, Vol. 45, No. 5, 1992, pp. 1-12.

[3] S. Horikawa, T. Furuhashi and Y. Uchikawa, “On Fuzzy Modeling Using Fuzzy Neural Networks with the Back Propagation Algorithm,” IEEE transactions on Neural Networks, Vol. 3, No. 5, 1992, pp. 801-806.

[4] D. Nauck and R. Kruse, “A Neuro-Fuzzy Method to Learn Fuzzy Classification Rules from Data,” Fuzzy Sets and Systems, Vol. 89, No. 3, 1997, pp. 277-288.

[5] J. S. R. Jang, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” IEEE Transactions on Systerms, Vol. 23, 1993, pp. 665-685.

[6] S. Mitra and S. K. Pal, “Fuzzy Multilayer Perceptron, Inferencing and Rule Generation,” IEEE Transactions on Neural Networks, Vol. 6, No. 1, 1995, pp. 51-63.

[7] W. L. Tung and C. Quek, “A Mamdani-Takagi-Sugeno Based Linguistic Neural-Fuzzy Inference System for Improved Interpretability-Accuracy Representation,” IEEE International Conference on Fuzzy Systems, Jeju Island, August 2009, pp. 367-372.

[8] W. L. Tung and C. Quek, “eFSM-A Novel Online Neur-al-Fuzzy Semantic Memory model,” IEEE Transactions on Neural Networks, Vol. 21, No. 1, 2010, pp. 136-157.

[9] P. K. Simpson, “Fuzzy Min-Max Neural Networks-Part 1: Classification,” IEEE Transactions on Neural Networks, Vol. 3, No. 5, 1992, pp. 776-786.

[10] P. K. Simpson, “Fuzzy Min-Max Neural Networks-Part 2: Clustering,” IEEE Transaction on Fuzzy Systems, Vol. 1, No. 1, 1992, pp. 32-45.

[11] R.-J. Wai and Z.-W. Yang, “Adaptive Fuzzy Neural Network Control Design via a T-S Fuzzy Model for a Robot Manipulator Including Actuator Dynamics,” IEEE Transactions on System, Man and Cybernetics-Part B, Vol. 38, No. 5, 2008, pp. 1326-1346.

[12] P. Sandeep and S. Kumar, “Subsethood Based Adaptive Linguistic Networks for Pattern Classification,” IEEE Transaction on System, man and cybernetics-part C: application and reviews, Vol. 33, No. 2, 2003, pp. 248-258.

[13] B. Kosko, “Fuzzy Engineering,” Prentice-Hall, Englewood Cliffs, New Jersey, 1997.

[14] K. Hornik, “Approximation Capabilities of Multilayer Feed forward Networks are Universal Approximators,” IEEE Transaction on Neural Networks, Vol. 2, No. 5, 1989, pp. 359-366.

[15] B. Kosko, “Fuzzy Systems as Universal Approximators,” IEEE Transactions on computers, Vol. 43, No. 11, 1994, pp. 1329-1333.

[16] C. T. Lin and Y. C. Lu, “A Neural Fuzzy System with Linguistic Teaching Signals,” IEEE Transactions Fuzzy Systems, Vol. 3, No. 2, 1995, pp. 169-189.

[17] L. X. Wang and J. M. Mendel, “Generating Fuzzy Rules from Numerical Data, with Application,” Technical Report 169, USC SIPI, University of Southern California, Los Angeles, January 1991.

[18] H. Narazaki and A. L. Ralescu, “An Improved Synthesis Method for Multilayered Neural Networks Using Qualitative Knowledge’s,” IEEE Transactions Fuzzy Systems, Vol. 1, No. 2, 1993, pp. 125-137.

[19] M. Russo, “FuGeNeSys-a Fuzzy Genetic Neural System for Fuzzy Modeling,” IEEE Transactions Fuzzy Systems, Vol. 6, No. 3, 1993, pp. 373-388.

[20] Y. Lin and G. A. Cunningham, “A New Approach to Fuzzy-Neural System Modeling,” IEEE Transactions Fuzzy Systems, Vol. 3, No. 2, 1995, pp. 190-198.