Abstract
The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. One of the defuzzification methods besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discussed.
The paper was supported in part by Grant-in-Aid for Young Scientists (B) #19700225 from Japan Society for the Promotion of Science (JSPS).
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References
Mamdani, E.H.: Application of fuzzy algorithms for control of simple dynamic plant. Proc. IEE 121(12), 1585–1588 (1974)
Tanaka, K., Sugeno, M.: Stability Analysis of Fuzzy Systems and Construction Procedure for Lyapunov Functions. Transactions of the Japan Society of Mechanical Engineers (C) 58(550), 1766–1772 (1992)
Hojo, T., Terano, T., Masui, S.: Fuzzy Feedback Control Rules Based on Optimality. Journal of Japan Society for Fuzzy Theory and Systems 5(5), 1200–1211 (1993)
Diamond, P.: Stability and periodicity in fuzzy differential equations. IEEE Trans. Fuzzy Syst. 8(5), 583–590 (2000)
Furuhashi, T.: Stability Analysis of Fuzzy Control Systems Based on Symbolic Expression. Journal of Japan Society for Fuzzy Theory and Systems 14(4), 357–365 (2002)
Gonda, E., Miyata, H., Ohkita, M.: Self-Tuning of Fuzzy Rules with Different Types of MSFs. Journal of Japan Society for Fuzzy Theory and Intelligent Informatics 16(6), 540–550 (2004)
Ishibuchi, H., Nii, M.: Generating Fuzzy Classification Rules from Trained Neural Networks. Journal of Japan Society for Fuzzy Theory and Systems 9(4), 512–524 (1997)
Nomura, H., Wakami, N.: A Method to Determine Fuzzy Inference Rules by a Genetic Algorithm. The Transactions of the Institute of Electronics, Information and Communication Engineers (A) J77-A(9), 1241–1249 (1994)
Shidama, Y., Yang, Y., Eguchi, M., Yamaura, H.: The compactness of a set of membership functions and its application to fuzzy optimal control. The Japan Society for Industrial and Applied Mathematics 6(1), 1–13 (1996)
Yang, Y., Wasaki, K., Eguchi, M., Shidama, Y., Kimura, M.: The Compactness of a Set of Fuzzy Membership Function in NBV and Its Application. IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences J82-A(4), 523–529 (1999)
Mitsuishi, T., Kawabe, J., Wasaki, K., Shidama, Y.: Optimization of Fuzzy Feedback Control Determined by Product-Sum-Gravity Method. Journal of Nonlinear and Convex Analysis 1(2), 201–211 (2000)
Mitsuishi, T., Kawabe, J., Wasaki, K., Shidama, Y.: Optimization of Fuzzy Feedback Control in L ∞ Space. In: Proc. International Conference on Fuzzy Systems (FUZZ-IEEE 2001), vol. 2, pp. 896–899 (2001)
Mitsuishi, T., Endou, N., Shidama, Y.: Continuity of Nakamori Fuzzy Model and Its Application to Optimal Feedback Control. In: Proc. IEEE International Conference on Systems, Man and Cybernetics, pp. 577–581 (2005)
Mizumoto, M.: Improvement of fuzzy control (II). In: Proc. 4th Fuzzy System Symposium, pp. 91–96 (1988)
Terano, T.: Practical Fuzzy Control Technology. IEICE, Tokyo (1991)
Mizumoto, M.: Improvement of fuzzy control (IV) - Case by product-sum-gravity method. In: Proc. 6th Fuzzy System Symposium, pp. 9–13 (1990)
Nakamori, Y., Ryoke, M.: Identification of fuzzy prediction models through hyperellipsoidal clustering. IEEE Transactions on Systems, Man and Cybernetics SMC 24(8), 1153–1173 (1994)
Miller, R.K., Michel, A.N.: Ordinary Differential Equations. Academic Press, New York (1982)
Riesz, F., Sz.-Nagy, B.: Functional Analysis. Dover Publications, New York (1990)
Dunford, N., Schwartz, J.T.: Linear Operators Part I: General Theory. John Wiley & Sons, New York (1988)
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Mitsuishi, T., Shidama, Y. (2009). Height Defuzzification Method on L ∞ Space. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds) Artificial Neural Networks – ICANN 2009. ICANN 2009. Lecture Notes in Computer Science, vol 5768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04274-4_62
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DOI: https://doi.org/10.1007/978-3-642-04274-4_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04273-7
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