Abstract
Fuzzy logic systems and feedforward neural networks are equivalent in essence. First, interpolation representations of fuzzy logic systems are introduced and several important conclusions are given. Then three important kinds of neural networks are defined, i. e. linear neural networks, rectangle wave neural networks and nonlinear neural networks. Then it is proved that nonlinear neural networks can be represented by rectangle wave neural networks. Based on the results mentioned above, the equivalence between fuzzy logic systems and feedforward neural networks is proved, which will be very useful for theoretical research or applications on fuzzy logic systems or neural networks by means of combining fuzzy logic systems with neural networks.
Similar content being viewed by others
References
Li Hongxing, The mathematical essence of fuzzy controls and fine fuzzy controllers, in Advances in Machine Intelligence and Soft-Computing (ed. Paul, P. Wang), Vol. IV, Durham: Bookwright Press, 1997, 55–74.
Li Hongxing, Interpolation mechanism of fuzzy control, Science in China, Ser. E, 1998, 41(3): 312.
Li Hongxing, Multifactorial functions in fuzzy sets theory, Fuzzy Sets and Systems, 1990, 35: 69.
Wang Goujun, On the logic foundation of fuzzy reasoning, Lecture Notes in Fuzzy Mathematics and Computer Science, Omaha: Creighton Univ., 1997, 4: 1.
Zhang Naiyao, Structure analysis of typical fuzzy controllers, Fuzzy Systems and Mathematics (in Chinese), 1997, 11 (2): 10.
Mizumoto, M., The improvement of fuzzy control algorithm, part 4: (+, ·)-centroid algorithm, Proceedings of Fuzzy Systems Theory (in Japanese), 1990, 6: 9.
Wang, P. Z., Li Hongxing, Fuzzy Information Processing and Fuzzy Computers, New York, Beijing: Science Press, 1997.
Terano, T., Asai, K., Sugeno, M., Fuzzy Systems Theory and Its Applications, Tokyo: Academic Press, Inc, 1992.
Sugeno, M., Fuzzy Control (in Japanese), Tokyo: Japane Industry Press, 1988.
Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man and Cybern., 1985, SMC-15: 1.
Pao, Y. H., Adaptive Pattern Recognition and Neural Networks, New York: Addison-Wesley Publishing Company, Inc., 1989.
Kosko, B., Neural Networks and Fuzzy Systems, Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1992.
Brown, M., Harris, C., Neurofuzzy Adaptive Modelling and Control, New York: Prentice Hall, 1994.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, H. Fuzzy logic systems are equivalent to feedforward neural networks. Sci. China Ser. E-Technol. Sci. 43, 42–54 (2000). https://doi.org/10.1007/BF02917136
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02917136