Fuzzy Logic Systems for Engineering: A Tutorial

Proceedings of the IEEE

Volumn 83, Issue 3, 1995, Pages 345-377

  Mendel, Jerry M ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL LINGUISTICS; COMPUTER SYSTEMS; CONSTRAINT THEORY; FEEDFORWARD NEURAL NETWORKS; LOGIC PROGRAMMING; MATHEMATICAL MODELS;

CASUALITY; FUZZY LOGIC SYSTEMS;

FUZZY SETS;

EID: 0029270928     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.364485     Document Type: Article

References (87)

1. C. B. Allendoerfer and C. O. Oakley, Principles of Mathematics. New York: McGraw-Hill, 1955.
2. D. L. Alspach and H. W. Sorenson, “Nonlinear Bayesian estimation using Gaussian sum approximations,” IEEE Trans. Automatic Control, vol. AC-17, pp. 439-448, Aug. 1972.
3. B. Baets and E. Kerre, “The generalized modus ponens and the triangular fuzzy data model,” Fuzzy Sets and Syst., vol. 59, pp. 305-317, 1993.
4. H. R. Berenji and P. Khedkar, “Learning and tuning fuzzy logic controllers through reinforcements,” IEEE Trans. Neural Networks, vol. 3, pp. 724-740, Sept. 1992.
5. J. Bezdek and S. K. Pal, Fuzzy Models for Pattern Recognition. New York: IEEE Press, 1992.
6. E. K. Blum and L. K. Li, “Approximation theory and feedforward networks,” Neural Networks, vol. 4, pp. 511-515, 1991.
7. P. P. Bonissone and K. S. Decker, “Selecting uncertainty calculi and granularity: An experiment in trading off precision and complexity,” in Uncertainty in Artificial Intelligence, L. N. Kanal and J. F. Lemmer, Eds. Amsterdam: Elsevier, 1986, pp. 217-247.
8. J. J. Buckley, “Universal fuzzy controllers,” Automatica, vol. 28, pp. 1245-1248, 1992.
9. P. Cheeseman, “An inquiry into computer understanding,” Comp. Intell., vol. 4, pp. 57-142, 1988 (with 22 commentaries/replies).
10. S. Chen, S. A. Billings, and W. Luo, “Orthogonal least squares methods and their application to nonlinear system identification,” Int. J. Contr., vol. 50, no. 5, pp. 1873-1896, 1989.
11. S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Networks, vol. 2, pp. 302-309, Feb. 1991.
12. P. Chu and J. M. Mendel, “First break refraction event picking using fuzzy logic systems,” USC SIPI Rep. #221, Sep., 1992; also, Proc. 2nd Int. Conf. on Fuzzy Systems; Mar./Apr. 1993, San Francisco, CA; also, IEEE Trans. Fuzzy Syst., vol. 2, pp. 255-266, 1994.
13. E. Cox, “Fuzzy fundamentals,” IEEE Spectrum, pp. 58-61, Oct. 1992.
14. E. Cox, The Fuzzy Systems Handbook. Cambridge, MA: AP Professional, 1994.
15. G. Cybenko, “Approximation by superpositions of sigmoidal function,” Mathematics of Control, Signals, and Systems, 1989.
16. J. A. Dickerson and B. Kosko, “Fuzzy function approximation with supervised ellipsoidal rules,” Proc. 1993 World Cong. on Neural Networks, vol. 2, pp. 9-17, July 1993.
17. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications. Orlando, FL: Academic, 1980.
18. D. Dubois and H. Prade, “A review of fuzzy set aggregation connectives,” Inf. Sciences, vol. 36, pp. 85-121, 1985.
19. A. W. F. Edwards, Likelihood. London, UK: Cambridge Univ. Press, 1972.
20. D. P. Filev and R. R. Yager, “A generalized defuzzification method via BAD distributions,” Int. J. Intell. Syst., vol. 6, pp. 687-697, 1991.
21. J. Hauser, S. Sastry, and P. Kokotovic, “Nonlinear control via approximate input-output linearization: The ball and beam example,” IEEE Trans. Autom. Contr., vol. AC-37, pp. 392-398, Mar. 1992.
22. H. Hellendoorn and C. Thomas, “Defuzzification in fuzzy controllers,” J. Intell. Syst., vol. 1, pp. 109-123, 1993.
23. S. Horikawa, T. Furahashi, and Y. Uchikawa, “On fuzzy modeling using fuzzy neural networks with back-propagation algorithm,” IEEE Trans. Neural Networks, vol. 3, pp. 801-806, Sept. 1992.
24. K. Hornik, “Some results on neural network approximation,” Neural Netwroks, vol. 6, pp. 1069-1072, 1993.
25. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, vol. 2, pp. 359-366, 1989.
26. Y. Iiguni, H. Sakai, and H. Tokumaru, “A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter,” IEEE Trans. Signal Processing, vol. 40, pp. 959-966, 1992.
27. J.-S. R. Jang, “Self-learning fuzzy controllers based on temporal back-propagation,” IEEE Trans. Neural Networks, vol. 3, pp. 714-723, Sept. 1992.
28. A. Kaufman and M. M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications. New York: Van Nostrand Reinhold, 1985.
29. Y. M. Kim and J. M. Mendel, “Fuzzy basis functions: Comparisons with other basis functions,” USC SIPI Rep. No. 229, Jan. 1993; also, accepted for publication in IEEE Trans. Fuzzy Systems, 1995.
30. J. B. Kiszka, M. E. Kochanska, and D. S. Sliwinska, “The influence of some parameters on the accuracy of fuzzy model,” in Industrial Applications of Fuzzy Control, M. Sugeno, Ed. Amsterdam: North-Holland, 1985, pp. 187-230.
31. J. B. Kiszka, M. E. Kochanska, and D. S. Sliwinska, “The influence of some parameters on the accuracy of a fuzzy model—Part I,” Fuzzy Sets Syst., vol. 15, pp. 111-128, 1985.
32. J. B. Kiszka, M. E. Kochanska, and D. S. Sliwinska, “The influence of some parameters on the accuracy of a fuzzy model—Part II,” Fuzzy Sets Syst., vol. 15, pp. 223-240, 1985.
33. G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty, and Information. Englewood Cliffs, NJ: Prentice Hall, 1988.
34. S. G. Kong and B. Kosko, “Comparison of fuzzy and neural truck backer-upper control systems,” Proc. IJCNN-90, vol. 3, pp. 349-358, June 1990.
35. B. Kosko, “Fuzziness versus probability,” Int. J. General Syst., vol. 17, pp. 211-240, 1990.
36. B. Kosko, Neural Network and Fuzzy Systems. A Dynamical Systems Approach to Machine Intelligence. Englewood Cliffs, NJ: Prentice-Hall, 1992.
37. B. Kosko, “Fuzzy systems as universal approximators,” IEEE Int. Conf. Fuzzy Syst., pp. 1153-1162, 1992.
38. B. Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic. New York: Hyperion, 1993.
39. B. Kosko, “Fuzzy systems as universal approximators,” IEEE Trans. Computers, 1994; an early version appears in Proc. 1st IEEE Int. Conf. on Fuzzy Systems, pp. 1153-1162, Mar. 1992.
40. B. Kosko and J. A. Dickerson, “Function approximation with additive fuzzy systems,” in Theoretical Aspects of Fuzzy Control, H. T. Nguyen, M. Sugeno, R. Tong, and R. Yager, Eds. New York: Wiley, 1994, chap. 12.
41. A. Lapedes and R. Farber, Nonlinear Signal Processing Using Neural Networks: Prediction and System Modeling, LA-UR-87-2662, Los Alamos, NM, 1987.
42. P. M. Larsen, “Industrial applications of fuzzy logic control,” Int. J. Man, Mach. Studies, vol. 12, no. 1, pp. 3-10, 1980.
43. M. Laviolette and J. W. Seaman, Jr., “The efficacy of fuzzy representations and uncertainty,” IEEE Trans. Fuzzy Syst., vol. 2, pp. 4-15, 1994.
44. C. C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller, part I,” IEEE Trans. Syst., Man, and Cybern., vol. SMC-20, no. 2, pp. 404-418, 1990.
45. C. C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller, Part II,” IEEE Trans. Syst., Man, and Cybern., vol. SMC-20, no. 2, pp. 419-435, 1990.
46. B. Y. Lindley, “Scoring rules and the inevitability of probability,” Int. Stat. Rev., vol. 50, pp. 1-26, 1982 (with seven commentaries/replies).
47. M. C. Mackey and L. Glass, “Oscillations and chaos in physiological control systems,” Science, vol. 197, pp. 287-289, 1987.
48. J. Maiers and Y. S. Sherif, “Applications of fuzzy set theory,” IEEE Trans. Syst., Man, and Cybern., vol. SMC-15, pp. 175-189, Jan./ Feb. 1985.
49. E. H. Mamdani, “Applications of fuzzy algorithms for simple dynamic plant,” Proc. IEE, vol. 121, pp. 1585-1588, 1974.
50. D. McNeill and P. Freilberger, Fuzzy Logic: The Discovery of a Revolutionary Computer Technology and How it is Changing Our World. New York: Simon and Schuster, 1992.
51. M. Mizumoto, “Comparison of various fuzzy reasoning methods,” Proc. 2nd IFSA Cong., Tokyo, Japan, pp. 2-7, July 1987.
52. J. Moody and C. J. Darken, “Fast learning in networks of locally-tuned processing units,” Neural Comp., vol. 1, pp. 281-294, 1989.
53. G. C. Mouzouris and J. M. Mendel, “Non-singleton fuzzy logic systems,” Proc. 1994 IEEE Conf. on Fuzzy Syst., Orlando, FL, June 1994.
54. G. C. Mouzouris and J. M. Mendel, Non-Singleton Fuzzy Logic Systems: Theory and Application, to be published.
55. D. Nguyen and B. Widrow, “The truck backer-upper: An example of self-learning in neural networks, IEEE Control Syst. Magazine, vol. 10, pp. 18-23, 1990.
56. P. Pacini and B. Kosko, “Comparison of fuzzy and Kalman filter target-tracking control systems,” in Neural Networks and Fuzzy Systems. Englewood Cliffs, NJ: Prentice-Hall, pp. 379-406.
57. T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE, vol. 78, pp. 1481-1497, Sept. 1990.
58. R. F. Popoli, “Objective and subjective knowledge in estimation,” Ph.D. dissertation, Univ. Southern California, Aug. 1989.
59. R. F. Popoli and J. M. Mendel, “Heuristically constrained estimation for intelligent signal processing,” in Advances in Geophysical Data Processing, vol. 3, M. Simaan and F. Aminzadeh, Eds. Greenwich, CT: JAI, 1989, pp. 107-134.
60. R. F. Popoli and J. M. Mendel, “Estimation using subjective knowledge with tracking applications,” IEEE Trans. Aerospace and Electron. Syst., vol. 29, pp. 610-623, 1993.
61. D. G. Schwartz, G. J. Klir, H. W. Lewis III, and Y. Ezawa, “Applications of fuzzy sets and approximate reasoning,” IEEE Proc., vol. 82, pp. 482-498, 1994.
62. S. Singhal and L. Wu, “Training feedforward networks with the extended Kalman filter,” Proc. IEEE Int. Conf. on Acoust., Speech and Signal Processing, pp. 1187-1190, May 1989.
63. D. F. Specht, “A general regression neural network,” IEEE Trans. Neural Networks, vol. 2, pp. 568-576, 1991.
64. M. S. Stachowicz and M. E. Kochanska, “Fuzzy modeling of the process,” Proc. 2nd IFSA Congress, Tokyo, Japan, pp. 86-89, July 1987.
65. M. Sugeno and G. T. Kang, “Fuzzy modeling and control of multilayer incinerator,” Fuzzy Sets and Syst., vol. 18, pp. 329-346, 1986.
66. M. Sugeno and T. Yasukawa, “A fuzzy-logic-based approach to qualitative modeling,” IEEE Trans. Fuzzy Systems, vol. 1, pp. 7-31, 1993.
67. T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Trans. Syst., Man and Cybernetics, vol. 15, pp. 116-132, 1985.
68. K. M. Tao, “A closer look at the radial basis function (RBF) networks,” Proc. 27th Asilomar Conf. on Signals, Systems and Computers, Pacific Grove, CA, Nov. 1993.
69. T. Terano, K. Asai, and M. Sugeno, Fuzzy Systems Theory and Its Applications. New York: Academic, 1992.
70. N. Vadiee and M. Jamshidi, “A tutorial on fuzzy rule-based expert systems (FRBES) models. 1: Mathematical foundations,” J. Intell. and Fuzzy Syst., vol. 1, pp. 171-188, 1993.
71. L. X. Wang, “Analysis and design of fuzzy systems,” Ph.D. dissertation, Univ. Southern California, Los Angeles, CA, 1992.
72. L. X. Wang, “Fuzzy systems are universal approximators,” Proc. IEEE Int. Conf. on Fuzzy Syst., San Diego, CA, 1992.
73. L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1994.
74. L. X. Wang and J. M. Mendel, “Generating fuzzy rules by learning from examples,” Proc. 6th IEEE Int. Symp. on Intell. Contr., pp. 263-268, 1991.
75. L. X. Wang and J. M. Mendel, “Generating fuzzy rules from numerical data, with applications,” USC SIPI Rep. No. 169, 1991; also in IEEE Trans. Systems, Man, and Cybern., vol. SMC-22, pp. 1414-1427, 1992.
76. L. X. Wang and J. M. Mendel, “Fuzzy basis functions, universal approximation, and orthogonal least squares learning,” IEEE Trans. Neural Networks, vol. 3, pp. 807-813, Sept. 1992.
77. L. X. Wang and J. M. Mendel, “Back-propagation of fuzzy systems as nonlinear dynamic system identifiers,” Proc. IEEE Int. Conf. on Fuzzy Syst., pp. 1409-1418, San Diego, CA, 1992.
78. R. L. Watrous, “Learning algorithms for connectionist networks: Applied gradient methods of nonlinear optimization,” Proc. IEEE 1st Int. Conf. on Neural Networks, vol. 2, pp. 619-627, June 1987.
79. R. R. Yager, “On the implication operator in fuzzy logic,” Inf. Sciences, vol. 31, pp. 141-164, 1983.
80. R. R. Yager and D. P. Filev, “Template-based fuzzy systems modeling,” J. Intell. and Fuzzy Syst., vol. 2, pp. 39-54, 1994.
81. R. R. Yager and D. P. Filev, Essentials of Fuzzy Modeling and Control. New York: Wiley, 1994.
82. J. Yen, R. Langari, and L. Zadeh, Eds., Industrial Applications of Fuzzy Logic and Intelligent Systems. New York: IEEE Press, 1995.
83. H. Ying, “Sufficient conditions on general fuzzy systems as function approximator,” Automatica, vol. 30, pp. 521-525, 1994.
84. L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, pp. 338-353, 1965.
85. L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Syst., Man and Cybern., vol. SMC-3, no. 1, pp. 28-44, 1973.
86. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning,” Inf. Sciences, vol. 8, pp. 199-249, and vol. 9, pp. 43-80, 1975.
87. H. J. Zimmermann. Fuzzy Set Theory and Its Applications, 2nd ed. Boston, MA: Kluwer, 1991.