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Defuzzification Using Area Method on L  ∞  Space

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Knowledge-Based and Intelligent Information and Engineering Systems (KES 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5712))

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Abstract

The mathematical framework for studying of a fuzzy approximate reasoning is presented. One of the defuzzification methods besides the center of gravity method which is the best well known defuzzification method is 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

  1. 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)

    Article  Google Scholar 

  2. 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)

    MathSciNet  Google Scholar 

  3. Diamond, P.: Stability and periodicity in fuzzy differential equations. IEEE Trans. Fuzzy Syst. 8(5), 583–590 (2000)

    Article  MATH  Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. 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)

    MathSciNet  MATH  Google Scholar 

  8. 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)

    Google Scholar 

  9. Mizumoto, M.: Improvement of fuzzy control (II). In: Proc. 4th Fuzzy System Symposium, pp. 91–96 (1988)

    Google Scholar 

  10. Terano, T.: Practical Fuzzy Control Technology. IEICE, Tokyo (1991)

    Google Scholar 

  11. Ohta, N., Harata, Y., Hayakawa, K.: A Fuzzy Inference LSI for an Automotive Control. R&D Review of Toyota CRDL 30(2), 45–55 (1995)

    Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. Miller, R.K., Michel, A.N.: Ordinary Differential Equations. Academic Press, New York (1982)

    MATH  Google Scholar 

  14. Riesz, F., Sz.-Nagy, B.: Functional Analysis. Dover Publications, New York (1990)

    MATH  Google Scholar 

  15. Dunford, N., Schwartz, J.T.: Linear Operators Part I: General Theory. John Wiley & Sons, New York (1988)

    MATH  Google Scholar 

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© 2009 Springer-Verlag Berlin Heidelberg

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Mitsuishi, T., Shidama, Y. (2009). Defuzzification Using Area Method on L  ∞  Space . In: Velásquez, J.D., Ríos, S.A., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based and Intelligent Information and Engineering Systems. KES 2009. Lecture Notes in Computer Science(), vol 5712. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04592-9_30

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  • DOI: https://doi.org/10.1007/978-3-642-04592-9_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04591-2

  • Online ISBN: 978-3-642-04592-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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