The min-max function differentiation and training of fuzzy neural networks

IEEE Transactions on Neural Networks

Volumn 7, Issue 5, 1996, Pages 1139-1150

  Zhang, Xinghu ^a   Hang, Chang Chieh ^b,c   Tan, Shaohua ^b,c   Wang, Pei Zhuang ^b  

^a DSO NATIONAL LABORATORIES   (Singapore)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c IEEE

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIATION (CALCULUS); FUNCTIONS; FUZZY SETS; LEARNING SYSTEMS; MATHEMATICAL OPERATORS; OPTIMIZATION; RANDOM PROCESSES;

FUZZY NEURAL NETWORKS; MIN MAX FUNCTIONS; REAL NUMBER FIELD;

NEURAL NETWORKS;

EID: 0030244497     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.536310     Document Type: Article

References (25)

1. R. J. Marks II, S. Oh, P. Arabshahi, T. P. Caudell, J. J. Choi, and B. G. Song, "Steepest descent adaptation of min-max fuzzy if-then rules," in Proc. IJCNN, Beijing, China, vol. III, 1992, pp. 471-477.
2. B. G. Song, R. J. Marks II, S. Oh, P. Arabshahi, T. P. Caudell, and J. J. Choi, "Adaptive membership function fusion and annihilation in fuzzy if-then rules," in Proc. 2nd IEEE Int. Conf. Fuzzy Syst. (FUZZ-IEEE'93), San Francisco, CA, vol. II, Mar. 1993, pp. 961-967.
3. H. Normura, I. Hayashi, and N. Wakami, "A learning method of fuzzy inference by descent method," in Proc. IEEE Int. Conf. Fuzzy Syst., FUZZ-IEEE'92, San Diego, CA, Mar. 8-12, 1992.
4. J. C. Bezdek, "Fuzzy models and computational neural networks," presented at IEEE Conf. Neural Networks Ocean Eng., Washington, D.C., Aug. 1991.
5. J. J. Buckley, Y. Hayashi, and E. Czogala, "On the equivalence of neural nets and fuzzy expert systems," Fuzzy Sets Syst., vol. 53, pp. 129-134, 1993.
6. M. M. Gupta, "Fuzzy neural computing systems," in Proc. 2nd Int. Conf. Fuzzy Logic Neural Networks, Japan, July 1992.
7. K. Hirota and W. Pedrycz, "Fuzzy logic neural networks: Design and computations," in Proc. Int. Joint Conf. Neural Networks, Singapore, Nov. 1991, pp. 18-21.
8. IEEE Trans. Neural Networks, special issue on Fuzzy Logic Neural Networks, vol. 3, 1992.
9. B. Widrow and M. A. Lehr, "Thirty years of adaptive neural networks: Perceptron, mahaline, and backpropagation," Proc. IEEE, vol. 78, no. 9, Sept. 1990.
10. J. M. Keller, R. R. Yager, and H. Tahani, "Neural network implementation of fuzzy logic," Fuzzy Sets Syst., vol. 45, pp. 1-12, 1992.
11. T. Khanna, Foundation of Neural Networks. Reading, MA: Addison-Wesley, 1990.
12. B. Kosko, Neural Networks and Fuzzy Systems Englewood Cliffs, NJ: Prentice-Hall, 1992.
13. L. X. Wang and J. M. Mendel, "Backpropagation fuzzy system as nonlinear dynamic system identifiers," in Proc. IEEE Int. Conf. Fuzzy Syst., FUZZ-IEEE'92, San Diego, CA, Mar. 8-12, 1992.
14. Y. H. Pao, Adaptive Pattern Recognition and Neural Networks. Reading, MA: Addison-Wesley, 1991.
15. W. Pedrycz, "Fuzzy neural networks and neurocomputations," Fuzzy Sets Syst., vol. 56, pp. 1-28, 1993.
16. E. Sanchez, "Fuzzy logic, expert systems and neural networks," SPIE issue on Stochastic and Neural Methods in Signal Proc., Image Proc., and Computer Vision, vol. 1569, pp. 474-483, 1991.
17. P. K. Simpson, "Fuzzy min-max neural networks - Part 1: Classification," IEEE Trans. Neural Networks, vol. 3. pp. 776-786, Sept. 1992.
18. _, "Fuzzy 'min-max neural networks - Part 2: Clustering," IEEE Trans. Fuzzy Syst., vol. 1, pp. 32-45, 1993.
19. P. Z. Wang and H. M. Zhang, "Truth-valued flow inference and its dynamic analysis," Beijing Shifan Daxue Xuebao, no. 1, pp. 1-12, 1989.
20. R. R. Yager, "Using fuzzy logic to build neural networks," in Proc. IFSA'91, Brussels, Belgium, 1991, vol. on Artificial Intell., pp. 210-213.
21. X. H. Zhang, F. Wong, and P. Z. Wang, "Decision-support neural networks and its applications in financial forecast," Bull. Studies and Exchanges on Fuzziness Applicat., no. 54, pp. 40-49, 1993.
22. X. H. Zhang, P. Z. Wang, Z. L. Shen, and X. T. Peng, "An adaptive fuzzy control model based on fuzzy neural networks," in Fuzzy Contr. Syst., A. Kandel, Ed. Boca Raton, FL: CRC, 1993, pp. 429-456.
23. X. H. Zhang, C. C. Hang, S. Tan, and P. Z. Wang, "The delta rule and learning for mix-max neural networks," in Proc. IEEE-ICNN'94, Orlando, FL, vol. 1, pp. 38-43.
24. M. K. Ochi, Applied Probability and Stochastic Process. New York: Wiley, 1990.
25. J. Lewin and M. Lewin, An Introduction to Mathematical Analysis. New York: McGraw-Hill, 1993.