A probabilistic fuzzy logic system: learning in the stochastic environment with incomplete dynamics
Authors: 
Han-Xiong Li, Zhi LiuAuthors Info & Claims
Pages 383 - 388
Abstract
A completely new type of fuzzy logic system will be developed from the existing fuzzy structure and applied to modeling and control of complex processes under incomplete dynamics in the manufacturing industry. Using a unique three-dimensional membership function (fuzz grade, time and probability), the probabilistic processing features can be added into the existing fuzzy configuration to construct a probabilistic fuzzy inference engine. Thus, this developed probabilistic fuzzy logic system (PFLS) is able to learn uncertain information in both fuzzy and stochastic nature. The proposed PFLS will be very suitable to modeling of the complex stochastic process with incomplete dynamics. All the existing learning theories and methods can be directly applied to the proposed PFLS to enhance its learning performance. Integrated into the fuzzy-PID structure, it will turn into a probabilistic fuzzy logic controller for the stochastic control. Successful application of the proposed PLFS to the selected industrial process will have a great impact on both academia and industry.
References
[1]
Michalewicz, Z.; Schmidt, M.; Michalewicz, M.; Chiriac, C.; "Case study: an intelligent decision support system", IEEE Intelligent Systems, 20: 44-49, 2005.
[2]
Ying, Hao, Feng Lin, Rodger D. MacArthur, Jonathan A. Cohn, Daniel C. Barth-Jones, Hong Ye, and Lawrence R. Crane, "A Fuzzy Discrete Event System Approach to Determining Optimal HIV/AIDS Treatment Regimens," IEEE Trans. on Information Technology in Biomedicine, 10: 663-676, 2006.
[3]
Raja Amirthalingam, Su Whan Sung, Jay H. Lee, "Two-step procedure for data-based modeling for inferential control applications", AIChE Journal, 46: 1974-1988, 2004.
[4]
Pearson, R. K.; "Outliers in process modeling and identification", IEEE Trans. on Control Systems Technology, 10: 55-63, 2002.
[5]
M. S. Grewal, A. P. Andrews. Kalman filtering : theory and practice Englewood Cliffs, N. J. : Prentice Hall, 1993.
[6]
Kazuo Tanaka and Hua.O Wang, Fuzzy control systems design and analysis, Wiley, 2001.
[7]
M. Brown, C. J. Harris, Neurofuzzy Adapttive Modeling and Control. Upper Saddle River, NJ: Prenice-Hall, 1994.
[8]
Sun-Yuan Kung; Taur, J.; Shang-Hung Lin; Synergistic modeling and applications of hierarchical fuzzy neural networks" Proceedings of the IEEE, vol. 87, no. 9, pp: 1550-1574, 1999.
[9]
Jang, J.-S. R.; Chuen-Tsai Sun; "Neuro-fuzzy modeling and control", Proceedings of the IEEE, 83: 378-406, 1995.
[10]
Mitter, S. K.; Filtering and stochastic control: a historical perspective, IEEE Control Systems Magazine, Volume 16, No. 3, pp: 67-76, 1996.
[11]
Dorato, P.; A historical review of robust control, IEEE Control Systems Magazine, Volume 7, No. 2, pp: 44-47, 1987.
[12]
N. N. Karnik, J. M. Mendel and Q. Liang, "Type-2 fuzzy logic systems," IEEE Trans. on Fuzzy Systems, vol. 7, no. 6, pp: 643-658, 1999.
[13]
C. H Wang, C. S Cheng, T. T Lee, "Dynamical Optimal Training for Interval Type-2 Fuzzy Neural Network (T2FNN)", IEEE Trans. on Syst. Man. Cybern Part B: vol. 34, no. 3, pp: 1462-1477, 2004.
[14]
Li, Q.; Leahy, R. M.; "Statistical Modeling and Reconstruction of Randoms Precorrected PET Data", IEEE Trans. on Medical Imaging, 25: 1565-1572, 2006.
[15]
B. Lee; L. Guo; Fuzzy Systems, "Optimal tracking design for stochastic fuzzy systems", IEEE Trans on Fuzzy Systems, vol. 11, no. 6, pp: 796- 813, 2003.
[16]
Z. Wang; Ho, D. W. C.; X. Liu, "A note on the robust stability of uncertain stochastic fuzzy systems with time-delays" IEEE Trans. on Syst. Man. Cybern, Part A, vol. 34, no. 4, pp: 570-576, 2004.
[17]
M. L. Puri and D. A. Ralescu, "Fuzzy random variables," J. Math. Anal. Appl., vol. 114, pp. 409-422, 1986.
[18]
de Cooman, G.; Aeyels, D, "A random set description of a possibility measure and its natural extension", IEEE Trans. on Syst. Man. Cybern, Part A, vol. 30, no. 2, pp: 124-130, 2000.
[19]
Romer, C.; Kandel, A. "Constraints on belief functions imposed by fuzzy random variables", IEEE Trans. on Syst. Man. Cybern, vol. 25, no. 1, pp: 86-99, 1995.
[20]
Kratschmer, V. "Constraints on belief functions imposed by fuzzy random variables: Some technical remarks on Romer-Kandel", IEEE Trans on Syst. Man. Cybern, Part B, vol. 28, no. 6, pp: 881-883, 1998.
[21]
Colubi, A, Fernandez-Garcia, C, Gil, M. A. "Simulation of random fuzzy variables: an empirical approach to statistical/probabilistic studies with fuzzy experimental data", IEEE Trans. on Fuzzy Systems, vol. 10, no. 3, pp: 384-390, 2003.
[22]
Z. Liu & H. X. Li, "A probabilistic fuzzy logic system for modeling and control", IEEE Trans Fuzzy Systems, Volume 13, No. 6, pp: 848-859, 2005.
[23]
H. X. Li & Zhi Liu; "A Probabilistic Neural-Fuzzy Learning System for Stochastic Modeling", IEEE Trans. on Fuzzy Systems, Volume 16, No. 4, pp: 898-908, 2008.
[24]
Emanuel Parzen, "On Estimation of a Probability Density Function and Mode", The Annals of Mathematical Statistics, vol. 33, pp. 1066-1076, 1962.
[25]
Sayan Mukherjee & Vladimir Vapnik, "Support vector method for multivariate density estimation", Technical Report, A.I. Memo No. 1653, MIT AI Lab, 1999.
[26]
J. Weston, A. Gammerman, M. Stitson, V. Vapnik, V. Vovk and C. Watkins. "Density Estimation using Support Vector Machines", Technical report CSD-TR-97-23, Royal Holloway University of London, UK(1997).
[27]
Ching-Chang Wong; Chia-Chong Chen; A hybrid clustering and gradient descent approach for fuzzy modeling. IEEE Trans. on Systems, Man, and Cybernetics, Part B, Volume 29, no. 6, pp: 686-693, 1999.
[28]
Celikyilmaz, A.; Burhan Turksen, I.; Enhanced Fuzzy System Models With Improved Fuzzy Clustering Algorithm, IEEE Trans. on Fuzzy Systems, Volume 16, no. 3, pp: 779-794, 2008.
[29]
Yager, R. R.; Cumulative distribution functions from Dempster-Shafer belief structures, IEEE Tran. on Systems, Man, and Cybernetics, Part B, Vol 34, no. 5, pp: 2080-2087, 2004.
[30]
R. Sutton and A. G. Barto, Reinforcement Learning: An Introduction, MIT Press, Cambridge, MA, 1998.
[31]
L. P. Kaelbling, M. L. Littman and A. W. Moore, "Reinforcement learning: a survey," Journal of Artificial Intelligence Research, Vol. 4, pp. 237-287, 1996.
[32]
N. H. C. Yung and C. Ye, "An intelligent mobile vehicle navigator based on fuzzy logic and reinforcement learning," IEEE Trans. on Systems Man and Cybernetics, Part B-Cybernetics, Vol. 29, pp. 314-321, 1999.
[33]
Mann G. K. I., B-G, Hu & R. G. Gosine, (1999), "Analysis of direct action fuzzy-PID controller structures", IEEE Trans. on Systems, Man and Cybernetics, 29B(3), 371-388
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Published In
October 2009
5232 pages
ISBN:9781424427932
Publisher
IEEE Press
Publication History
Published: 11 October 2009
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