Continuity of Defuzzification and Its Application to Fuzzy Control
The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) 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.
[1] L. A. Zadeh, "Fuzzy Sets", Information and Control, Vol. 8, pp.338-353,
1965.
[2] E. H. Mamdani, "Application of fuzzy algorithms for control of simple
dynamic plant", Proc. IEE 121, No. 12, pp.1585-1588, 1974.
[3] P. Diamond, "Stability and periodicity in fuzzy differential equations",
IEEE Trans. Fuzzy Syst., Vol. 8, pp. 583-590, Oct. 2000.
[4] T. Hojo, T. Terano and S. Masui, "Fuzzy Feedback Control Rules Based
on Optimality", Journal of Japan Society for Fuzzy Theory and Systems,
Vol.5, No.5, pp. 1200-1211, 1993, in Japanese.
[5] K. Tanaka and M. Sugeno, "Stability Analysis of Fuzzy Systems and
Construction Procedure for Lyapunov Functions", Transactions of the
Japan Society of Mechanical Engineers. C, Vol. 58, No. 550, pp. 1766-
1772, 1992, in Japanese.
[6] T. Hojo, T. Terano and S. Masui, "Stability Analysis of Fuzzy Control
Systems Based on Phase Plane Analysis", Journal of Japan Society for
Fuzzy Theory and Systems, Vol.4, No.6, pp. 127-140, 1992, in Japanese.
[7] T. Furuhashi, "Stability Analysis of Fuzzy Control Systems Based on
Symbolic Expression", Journal of Japan Society for Fuzzy Theory and
Systems, Vol.14, No.4, pp. 357-365, 2002, in Japanese.
[8] H. Ishibuchi and M. Nii, "Generating Fuzzy Classification Rules from
Trained Neural Networks", Journal of Japan Society for Fuzzy Theory
and Systems, Vol.9, No.4, pp. 512-524, 1997, in Japanese.
[9] H. Nomura and N. Wakami, "A Method to Determine Fuzzy Inference
Rules by a Genetic Algorithm", The Transactions of the Institute of
Electronics, Information and Communication Engineers. A, Vol. J77-A,
No. 9, pp. 1241-1249, 1994, in Japanese.
[10] Y. Yang, K. Wasaki, M. Eguchi, Y. Shidama and M. Kimura, "The
Compactness of a Set of Fuzzy Membership Function in NBV and Its
Application", IEICE TRANSACTIONS on Fundamentals of Electronics,
Communications and Computer Sciences, Vol. J82-A, No. 4, pp.523-
529, 1999, in Japanese.
[11] T. Mitsuishi, J. Kawabe, K. Wasaki and Y. Shidama, "Optimization of
Fuzzy Feedback Control Determined by Product-Sum-Gravity Method",
Journal of Nonlinear and Convex Analysis, Vol. 1, No. 2, pp.201-211,
2000.
[12] T. Mitsuishi, J. Kawabe, K. Wasaki and Y. Shidama, "Optimization of
Fuzzy Feedback Control in L8 Space", Proc. International Conference
on Fuzzy Systems (FUZZ-IEEE2001), Vol. 2, pp.896-899, 2001.
[13] T. Mitsuishi, N. Endou and Y. Shidama, "Continuity of Nakamori Fuzzy
Model and Its Application to Optimal Feedback Control", Proc. of IEEE
International Conference on Systems, Man and Cybernetics (SMC2005),
pp.577-581, 2005.
[14] M. Mizumoto, "Improvement of fuzzy control (II) ", Proc. 4th Fuzzy
System Symposium, pp.91-96, 1988, in Japanese.
[15] M. Mizumoto, "Improvement of fuzzy control (IV) - Case by productsum-
gravity method -", Proc. 6th Fuzzy System Symposium, pp.9-13,
1990, in Japanese.
[16] R. K. Miller and A. N. Michel, " Ordinary Differential Equations"
Academic Press, New York, 1982.
[17] Frigyes Riesz and Bela Sz.-Nagy, "Functional Analysis", Dover Publications,
New York, 1990.
[18] N. Dunford and J. T. Schwartz, "Linear Operators Part I: General
Theory", John Wiley & Sons, New York, 1988.
[19] T. Terano, "Practical Fuzzy Control Technology", IEICE, Tokyo, 1991,
in Japanese.
[1] L. A. Zadeh, "Fuzzy Sets", Information and Control, Vol. 8, pp.338-353,
1965.
[2] E. H. Mamdani, "Application of fuzzy algorithms for control of simple
dynamic plant", Proc. IEE 121, No. 12, pp.1585-1588, 1974.
[3] P. Diamond, "Stability and periodicity in fuzzy differential equations",
IEEE Trans. Fuzzy Syst., Vol. 8, pp. 583-590, Oct. 2000.
[4] T. Hojo, T. Terano and S. Masui, "Fuzzy Feedback Control Rules Based
on Optimality", Journal of Japan Society for Fuzzy Theory and Systems,
Vol.5, No.5, pp. 1200-1211, 1993, in Japanese.
[5] K. Tanaka and M. Sugeno, "Stability Analysis of Fuzzy Systems and
Construction Procedure for Lyapunov Functions", Transactions of the
Japan Society of Mechanical Engineers. C, Vol. 58, No. 550, pp. 1766-
1772, 1992, in Japanese.
[6] T. Hojo, T. Terano and S. Masui, "Stability Analysis of Fuzzy Control
Systems Based on Phase Plane Analysis", Journal of Japan Society for
Fuzzy Theory and Systems, Vol.4, No.6, pp. 127-140, 1992, in Japanese.
[7] T. Furuhashi, "Stability Analysis of Fuzzy Control Systems Based on
Symbolic Expression", Journal of Japan Society for Fuzzy Theory and
Systems, Vol.14, No.4, pp. 357-365, 2002, in Japanese.
[8] H. Ishibuchi and M. Nii, "Generating Fuzzy Classification Rules from
Trained Neural Networks", Journal of Japan Society for Fuzzy Theory
and Systems, Vol.9, No.4, pp. 512-524, 1997, in Japanese.
[9] H. Nomura and N. Wakami, "A Method to Determine Fuzzy Inference
Rules by a Genetic Algorithm", The Transactions of the Institute of
Electronics, Information and Communication Engineers. A, Vol. J77-A,
No. 9, pp. 1241-1249, 1994, in Japanese.
[10] Y. Yang, K. Wasaki, M. Eguchi, Y. Shidama and M. Kimura, "The
Compactness of a Set of Fuzzy Membership Function in NBV and Its
Application", IEICE TRANSACTIONS on Fundamentals of Electronics,
Communications and Computer Sciences, Vol. J82-A, No. 4, pp.523-
529, 1999, in Japanese.
[11] T. Mitsuishi, J. Kawabe, K. Wasaki and Y. Shidama, "Optimization of
Fuzzy Feedback Control Determined by Product-Sum-Gravity Method",
Journal of Nonlinear and Convex Analysis, Vol. 1, No. 2, pp.201-211,
2000.
[12] T. Mitsuishi, J. Kawabe, K. Wasaki and Y. Shidama, "Optimization of
Fuzzy Feedback Control in L8 Space", Proc. International Conference
on Fuzzy Systems (FUZZ-IEEE2001), Vol. 2, pp.896-899, 2001.
[13] T. Mitsuishi, N. Endou and Y. Shidama, "Continuity of Nakamori Fuzzy
Model and Its Application to Optimal Feedback Control", Proc. of IEEE
International Conference on Systems, Man and Cybernetics (SMC2005),
pp.577-581, 2005.
[14] M. Mizumoto, "Improvement of fuzzy control (II) ", Proc. 4th Fuzzy
System Symposium, pp.91-96, 1988, in Japanese.
[15] M. Mizumoto, "Improvement of fuzzy control (IV) - Case by productsum-
gravity method -", Proc. 6th Fuzzy System Symposium, pp.9-13,
1990, in Japanese.
[16] R. K. Miller and A. N. Michel, " Ordinary Differential Equations"
Academic Press, New York, 1982.
[17] Frigyes Riesz and Bela Sz.-Nagy, "Functional Analysis", Dover Publications,
New York, 1990.
[18] N. Dunford and J. T. Schwartz, "Linear Operators Part I: General
Theory", John Wiley & Sons, New York, 1988.
[19] T. Terano, "Practical Fuzzy Control Technology", IEICE, Tokyo, 1991,
in Japanese.
@article{"International Journal of Information, Control and Computer Sciences:60687", author = "Takashi Mitsuishi and Kiyoshi Sawada and Yasunari Shidama", title = "Continuity of Defuzzification and Its Application to Fuzzy Control", abstract = "The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) 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.
", keywords = "Fuzzy approximate reasoning, defuzzification, area method, height method.", volume = "3", number = "2", pages = "447-5", }
