Improving Convergence of Parameter Tuning Process of the Additive Fuzzy System by New Learning Strategy
An additive fuzzy system comprising m rules with
n inputs and p outputs in each rule has at least t m(2n + 2 p + 1)
parameters needing to be tuned. The system consists of a large
number of if-then fuzzy rules and takes a long time to tune its
parameters especially in the case of a large amount of training data
samples. In this paper, a new learning strategy is investigated to cope
with this obstacle. Parameters that tend toward constant values at the
learning process are initially fixed and they are not tuned till the end
of the learning time. Experiments based on applications of the
additive fuzzy system in function approximation demonstrate that the
proposed approach reduces the learning time and hence improves
convergence speed considerably.
[1] B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems
Approach to Machine Intelligence. Prentice Hall, 1991.
[2] B. Kosko, "Fuzzy systems as universal approximators", IEEE
Transactions on Computers, vol. 43, no. 11, 1994, pp. 1329-1333.
[3] B. Kosko, "Combining fuzzy systems". Proceedings of the IEEE
International Conference on Fuzzy Systems (IEEE FUZZ-95), 1995, pp.
1855-1863.
[4] B. Kosko, "Optimal fuzzy rules cover extrema". International Journal of
Intelligent Systems, vol. 10, no. 2, 1995, pp. 249-255.
[5] B. Kosko, Fuzzy Engineering. Prentice Hall, 1996.
[6] B. Kosko, "Global stability of generalized additive fuzzy systems",
IEEE Transactions on Systems, Man, and Cybernetics, vol. 28, no. 3,
1998, pp. 441-452.
[7] G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and
Applications, Prentice Hall, Upper Saddle River, NJ, USA, 1995.
[8] J.A. Dickerson and B. Kosko, "Fuzzy function approximation with
supervised ellipsoidal learning", World Congress on Neural Networks,
vol. 2, 1993, pp. 9-13.
[9] J.A. Dickerson and B. Kosko, "Fuzzy function approximation with
ellipsoidal rules", IEEE Transactions Systems, Man, and Cybernetics,
vol. 26, no. 4, 1996, pp. 542-560.
[10] S. Mitaim and B. Kosko, "What is the best shape for a fuzzy set in
function approximation?", Proceeding of the 5th IEEE International
Conference on Fuzzy Systems, vol. 2, 1996, pp. 1237-1243.
[11] S. Mitaim and B. Kosko, "Adaptive joint fuzzy sets for function
approximation", Proceeding of IEEE International Conference on
Neural Networks, vol. 1, 1997, pp. 537-542.
[12] S. Mitaim and B. Kosko, "The shape of fuzzy sets in adaptive function
approximation", IEEE Transactions on Fuzzy Systems, vol. 9, no. 4,
2001, pp. 637-656.
[1] B. Kosko, Neural Networks and Fuzzy Systems: A Dynamical Systems
Approach to Machine Intelligence. Prentice Hall, 1991.
[2] B. Kosko, "Fuzzy systems as universal approximators", IEEE
Transactions on Computers, vol. 43, no. 11, 1994, pp. 1329-1333.
[3] B. Kosko, "Combining fuzzy systems". Proceedings of the IEEE
International Conference on Fuzzy Systems (IEEE FUZZ-95), 1995, pp.
1855-1863.
[4] B. Kosko, "Optimal fuzzy rules cover extrema". International Journal of
Intelligent Systems, vol. 10, no. 2, 1995, pp. 249-255.
[5] B. Kosko, Fuzzy Engineering. Prentice Hall, 1996.
[6] B. Kosko, "Global stability of generalized additive fuzzy systems",
IEEE Transactions on Systems, Man, and Cybernetics, vol. 28, no. 3,
1998, pp. 441-452.
[7] G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and
Applications, Prentice Hall, Upper Saddle River, NJ, USA, 1995.
[8] J.A. Dickerson and B. Kosko, "Fuzzy function approximation with
supervised ellipsoidal learning", World Congress on Neural Networks,
vol. 2, 1993, pp. 9-13.
[9] J.A. Dickerson and B. Kosko, "Fuzzy function approximation with
ellipsoidal rules", IEEE Transactions Systems, Man, and Cybernetics,
vol. 26, no. 4, 1996, pp. 542-560.
[10] S. Mitaim and B. Kosko, "What is the best shape for a fuzzy set in
function approximation?", Proceeding of the 5th IEEE International
Conference on Fuzzy Systems, vol. 2, 1996, pp. 1237-1243.
[11] S. Mitaim and B. Kosko, "Adaptive joint fuzzy sets for function
approximation", Proceeding of IEEE International Conference on
Neural Networks, vol. 1, 1997, pp. 537-542.
[12] S. Mitaim and B. Kosko, "The shape of fuzzy sets in adaptive function
approximation", IEEE Transactions on Fuzzy Systems, vol. 9, no. 4,
2001, pp. 637-656.
@article{"International Journal of Information, Control and Computer Sciences:55677", author = "Thi Nguyen and Lee Gordon-Brown and Jim Peterson and Peter Wheeler", title = "Improving Convergence of Parameter Tuning Process of the Additive Fuzzy System by New Learning Strategy", abstract = "An additive fuzzy system comprising m rules with
n inputs and p outputs in each rule has at least t m(2n + 2 p + 1)
parameters needing to be tuned. The system consists of a large
number of if-then fuzzy rules and takes a long time to tune its
parameters especially in the case of a large amount of training data
samples. In this paper, a new learning strategy is investigated to cope
with this obstacle. Parameters that tend toward constant values at the
learning process are initially fixed and they are not tuned till the end
of the learning time. Experiments based on applications of the
additive fuzzy system in function approximation demonstrate that the
proposed approach reduces the learning time and hence improves
convergence speed considerably.", keywords = "Additive fuzzy system, improving convergence,
parameter learning process, unsupervised learning.", volume = "2", number = "9", pages = "3024-5", }