Optimal Size Fuzzy Models
Tamás D. Gedeon*, László T. Kóczy**, and Alessandro Zorat***
*Dept. of Computer Science, Australian National University, Canberra 0200, Australia
**Dept. of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Sztocek u. 2, H-1111 Budapest, Hungary
***Dept. of Information and Communication Technologies, University of Trento, Via Sommarive 14, Povo, I-38100 Italy
Approximate models using fuzzy rule bases can be made more precise by suitably increasing the size of the rule base and decreasing uncertainty in the rules. A large rule base, however, requires more time for its evaluation and hence the problem arises of determining the size that is good enough for the task at hand, but allows as fast as possible reasoning using the rule base. This trade-off between computation time and precision is significant whenever a prediction is made which can become “out of date” or “too old” if not used in time. The trade off is considered here in the context of tracking a moving target. In this problem, a higher degree of accuracy results in tighter precision of determining target location, but at the cost of longer computation time, during which the target can move further away, thus ultimately requiring a longer search for exact target localisation. This paper examines the problem of determining the optimal rule base size that will yield a minimum total time required to repeatedly re-acquire the moving target, as done by a cat that plays with a mouse. While this problem has no known solution in its general formulation, solutions are shown here for specific contexts.
-  D. G. Burkhardt and P. P. Bonissone, “Automated fuzzy knowledge base generation and tuning,” IEEE Int. Conf. on Fuzzy Systems, San Diego, pp. 179-196, 1992.
-  J. L. Castro, “Fuzzy logic controllers are universal approximators,” IEEE Tr. on SMC 25, pp. 629-635, 1995.
-  D. Drinkov, H. Hellendoorn, and M. Reinfrank, “An Introduction to Fuzzy Control,” Springer, Berlin, etc., 1993.
-  L. T. Kóczy, “Compression of fuzzy rule bases by interpolation,” Proceedings of the First Asian Fuzzy Systems Symposium, Singapore, pp. 500-507, 1993.
-  L. T. Kóczy, A. Zorat, and T. D. Gedeon, “The Cat and Mouse Problem – optimising the size of fuzzy rule bases,” Proceedings of CIFT’95, Trento, pp. 139-151, 1995.
-  W. Pedrycz, “Fuzzy Control and Fuzzy Systems,” 2nd edition, J. Wiley, Chichester, 1992.
-  M. Sugeno and T. Yasukawa, “A fuzzy-logic-based approach to qualitative modelling,” IEEE Tr. on Fuzzy Systems 1, pp. 7-31, 1993.
-  L. X. Wang, “Adaptive Fuzzy Systems and Control,” Prentice Hall, Englewood Cliffs, N.J., 1994.
-  R. Yager and D. Filev, “Essentials of Fuzzy Modelling and Control,” J. Wiley, Chichester, 2004.
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